In Ho Jeon - Academia.edu (original) (raw)

Papers by In Ho Jeon

Research paper thumbnail of On operators satisfying T∗∣T2∣T⩾T∗∣T∣2T

Linear Algebra and its Applications, 2006

Let T be a bounded linear operator on a complex Hilbert space H. In this paper we introduce the c... more Let T be a bounded linear operator on a complex Hilbert space H. In this paper we introduce the class, denoted QA, of operators satisfying T * |T 2 |T T * |T | 2 T and we prove basic structural properties of these operators. Using these results, we also prove that if E is the Riesz idempotent for a non-zero isolated point λ 0 of the spectrum of T ∈ QA, then E is self-adjoint, and we give a necessary and sufficient condition for T ⊗ S to be in QA when T and S are both non-zero operators.

Research paper thumbnail of On a spectral property of analytic operators

Tsukuba Journal of Mathematics, 1996

Research paper thumbnail of CONTINUITY OF THE SPECTRUM ON (classA)*

Korean Journal of Mathematics, 2013

Let (classA) * denotes the class of operators satisfying |T 2 | ≥ |T * | 2. In this paper, we sho... more Let (classA) * denotes the class of operators satisfying |T 2 | ≥ |T * | 2. In this paper, we show that the spectrum is continuous on (classA) * .

Research paper thumbnail of Joint Spectra Of Doubly Commuting $ n $-Tuples Of Operators And Their Aluthge Transforms

Nihonkai Mathematical Journal, 2000

Research paper thumbnail of On p-quasihyponormal operators and quasisimilarity

Mathematical Inequalities & Applications, 2003

Research paper thumbnail of On Quasisimilarity for Log-Hyponormal Operators

Glasgow Mathematical Journal, 2004

In this paper we show that the normal parts of quasisimilar loghyponormal operators are unitarily... more In this paper we show that the normal parts of quasisimilar loghyponormal operators are unitarily equivalent. A Fuglede-Putnam type theorem for log-hyponormal operators is proved. Also, it is shown that a log-hyponormal operator that is quasisimilar to an isometry is unitary and that a log-hyponormal spectral operator is normal.

Research paper thumbnail of Weyl's theorem through local spectral theory

Glasgow Mathematical Journal, 2002

In this paper, we show that Weyl's theorem holds for operators having the single valued extension... more In this paper, we show that Weyl's theorem holds for operators having the single valued extension property and quasisimilarity preserves Weyl's theorem for these operators under some assumptions for spectral subsets, respectively.

Research paper thumbnail of Weyl's theorem for f(T{\hskip1}) when T is a dominant operator

Glasgow Mathematical Journal, 2001

Let T be a dominant operator that is a quasi-affine transform of an M-hyponormal operator. In thi... more Let T be a dominant operator that is a quasi-affine transform of an M-hyponormal operator. In this paper we show that if f is a function analytic on a neighborhood of the spectrum of T, then Weyl's theorem holds for fðT Þ.

Research paper thumbnail of Polaroid operators and Weyl’s theorem

Proceedings of the American Mathematical Society, 2003

Research paper thumbnail of k-TH ROOTS OF p-HYPONORMAL OPERATORS

Bulletin of the Korean Mathematical Society, 2005

Research paper thumbnail of Continuity of the Spectrum on a Class A(Κ)

Korean Journal of Mathematics, 2013

Let T be a bounded linear operator on a complex Hilbert space H. An operator T is called class A ... more Let T be a bounded linear operator on a complex Hilbert space H. An operator T is called class A operator if |T 2 | ≥ |T | 2 and is called class A(k) operator if (T * |T | 2k T) 1 k+1 ≥ |T | 2 for a positive number k. In this paper, we show that σ is continuous when restricted to the set of class A(k) operators.

Research paper thumbnail of On Quasi-Class a Operators

Korean Journal of Mathematics, 2011

Let f be an analytic function defined on an open neighbourhood U of σ(T) such that f is non-const... more Let f be an analytic function defined on an open neighbourhood U of σ(T) such that f is non-constant on the connected components of U. We generalize a theorem of Sheth [10] to f (T) ∈ QA.

Research paper thumbnail of On Operators with an Absolute Value Condition

Journal of the Korean Mathematical Society, 2004

Research paper thumbnail of ON k-QUASI-CLASS A CONTRACTIONS

Korean Journal of Mathematics, 2014

A bounded linear Hilbert space operator T is said to be k-quasi-class A operator if it satisfy th... more A bounded linear Hilbert space operator T is said to be k-quasi-class A operator if it satisfy the operator inequality T * k |T 2 |T k ≥ T * k |T | 2 T k for a non-negative integer k. It is proved that if T is a k-quasi-class A contraction, then either T has a nontrivial invariant subspace or T is a proper contraction and the nonnegative operator D = T * k (|T 2 | − |T | 2)T k is strongly stable.

Research paper thumbnail of On ∗-paranormal contractions and properties for ∗-class A operators

Linear Algebra and its Applications, 2012

C .0-contraction Tensor product An operator T ∈ B(H) is called a *-class A operator if |T 2 | |T ... more C .0-contraction Tensor product An operator T ∈ B(H) is called a *-class A operator if |T 2 | |T * | 2 , and T is said to be *-paranormal if T * x 2 T 2 x for every unit vector x in H. In this paper, we show that *-paranormal contractions are the direct sum of a unitary and a C .0 completely non-unitary contraction. Also, we consider the tensor products of *-class A operators.

Research paper thumbnail of On p-quasi-hyponormal operators

Linear Algebra and its Applications, 2007

A Hilbert space operator A ∈ B(H) is said to be p-quasi-hyponormal for some 0 < p 1, A ∈ p − QH ,... more A Hilbert space operator A ∈ B(H) is said to be p-quasi-hyponormal for some 0 < p 1, A ∈ p − QH , if A * (|A| 2p − |A * | 2p)A 0. If H is infinite dimensional, then operators A ∈ p − QH are not supercyclic. Restricting ourselves to those A ∈ p − QH for which A −1 (0) ⊆ A * −1 (0), A ∈ p * − QH , a necessary and sufficient condition for the adjoint of a pure p * − QH operator to be supercyclic is proved. Operators in p * − QH satisfy Bishop's property (β). Each A ∈ p * − QH has the finite ascent property and the quasinilpotent part H 0 (A − λI) of A equals (A − λI) −1 (0) for all complex numbers λ; hence f (A) satisfies Weyl's theorem, and f (A *) satisfies a-Weyl's theorem, for all non-constant functions f which are analytic on a neighborhood of σ (A). It is proved that a Putnam-Fuglede type commutativity theorem holds for operators in p * − QH .

Research paper thumbnail of On quasi-class contractions

Linear Algebra and its Applications, 2012

Let QA denote the class of bounded linear Hilbert space operators T which satisfy the operator in... more Let QA denote the class of bounded linear Hilbert space operators T which satisfy the operator inequality T * |T 2 |T ≥ T * |T| 2 T. It is proved that if T ∈ QA is a contraction, then either T has a nontrivial invariant subspace or T is a proper contraction and the nonnegative operator D = T * (|T 2 | − |T| 2)T is strongly stable. It is shown that if T ∈ QA is a contraction with Hilbert-Schmidt defect operator such that T −1 (0) ⊆ T * −1 (0), then T is completely non-normal if and only if T ∈ C 10 , and a commutativity theorem is proved for contractions T ∈ QA. Let T u and T c denote the unitary part and the cnu part of a contraction T, respectively. We prove that if A = A u ⊕ A c and B = B u ⊕ B c are QA-contractions such that μ A c < ∞, then A and B are quasi-similar if and only A u and B u are unitarily equivalent and A c and B c are quasi-similar.

Research paper thumbnail of Continuity of the spectrum on a class of upper triangular operator matrices

Journal of Mathematical Analysis and Applications, 2010

It is proved that the set theoretic function σ , the spectrum, is continuous on the set C(i) ⊂ B(... more It is proved that the set theoretic function σ , the spectrum, is continuous on the set C(i) ⊂ B(H i) of operators A for which σ (A) = {0} implies A is nilpotent (possibly, the 0 operator) and A • = λ X 0 B (A • −λ) −1 (0) {(A • −λ) −1 (0)} ⊥ at every non-zero λ ∈ σ p (A •) for some operators X and B such that λ / ∈ σ p (B) and σ (A •) = {λ} ∪ σ (B). If C S (m) denotes the set of upper triangular operator matrices A = (A ij) m i, j=1 ∈ B(n i=1 H i), where A ii ∈ C(i) and A ii has SVEP for all 1 i m, then σ is continuous on C S (m). It is observed that a considerably large number of the more commonly considered classes of Hilbert space operators constitute sets C(i) and have SVEP.

Research paper thumbnail of Generalized Browder's and Weyl's theorems for left and right multiplication operators

Journal of Mathematical Analysis and Applications, 2010

The main objective of this work is to study generalized Browder's and Weyl's theorems for the mul... more The main objective of this work is to study generalized Browder's and Weyl's theorems for the multiplication operators L A and R B and for the elementary operator τ AB = L A R B .

Research paper thumbnail of Weyl's Theorem for Operator Matrices and the Single Valued Extension Property

Glasgow Mathematical Journal, 2006

Research paper thumbnail of On operators satisfying T∗∣T2∣T⩾T∗∣T∣2T

Linear Algebra and its Applications, 2006

Let T be a bounded linear operator on a complex Hilbert space H. In this paper we introduce the c... more Let T be a bounded linear operator on a complex Hilbert space H. In this paper we introduce the class, denoted QA, of operators satisfying T * |T 2 |T T * |T | 2 T and we prove basic structural properties of these operators. Using these results, we also prove that if E is the Riesz idempotent for a non-zero isolated point λ 0 of the spectrum of T ∈ QA, then E is self-adjoint, and we give a necessary and sufficient condition for T ⊗ S to be in QA when T and S are both non-zero operators.

Research paper thumbnail of On a spectral property of analytic operators

Tsukuba Journal of Mathematics, 1996

Research paper thumbnail of CONTINUITY OF THE SPECTRUM ON (classA)*

Korean Journal of Mathematics, 2013

Let (classA) * denotes the class of operators satisfying |T 2 | ≥ |T * | 2. In this paper, we sho... more Let (classA) * denotes the class of operators satisfying |T 2 | ≥ |T * | 2. In this paper, we show that the spectrum is continuous on (classA) * .

Research paper thumbnail of Joint Spectra Of Doubly Commuting $ n $-Tuples Of Operators And Their Aluthge Transforms

Nihonkai Mathematical Journal, 2000

Research paper thumbnail of On p-quasihyponormal operators and quasisimilarity

Mathematical Inequalities & Applications, 2003

Research paper thumbnail of On Quasisimilarity for Log-Hyponormal Operators

Glasgow Mathematical Journal, 2004

In this paper we show that the normal parts of quasisimilar loghyponormal operators are unitarily... more In this paper we show that the normal parts of quasisimilar loghyponormal operators are unitarily equivalent. A Fuglede-Putnam type theorem for log-hyponormal operators is proved. Also, it is shown that a log-hyponormal operator that is quasisimilar to an isometry is unitary and that a log-hyponormal spectral operator is normal.

Research paper thumbnail of Weyl's theorem through local spectral theory

Glasgow Mathematical Journal, 2002

In this paper, we show that Weyl's theorem holds for operators having the single valued extension... more In this paper, we show that Weyl's theorem holds for operators having the single valued extension property and quasisimilarity preserves Weyl's theorem for these operators under some assumptions for spectral subsets, respectively.

Research paper thumbnail of Weyl's theorem for f(T{\hskip1}) when T is a dominant operator

Glasgow Mathematical Journal, 2001

Let T be a dominant operator that is a quasi-affine transform of an M-hyponormal operator. In thi... more Let T be a dominant operator that is a quasi-affine transform of an M-hyponormal operator. In this paper we show that if f is a function analytic on a neighborhood of the spectrum of T, then Weyl's theorem holds for fðT Þ.

Research paper thumbnail of Polaroid operators and Weyl’s theorem

Proceedings of the American Mathematical Society, 2003

Research paper thumbnail of k-TH ROOTS OF p-HYPONORMAL OPERATORS

Bulletin of the Korean Mathematical Society, 2005

Research paper thumbnail of Continuity of the Spectrum on a Class A(Κ)

Korean Journal of Mathematics, 2013

Let T be a bounded linear operator on a complex Hilbert space H. An operator T is called class A ... more Let T be a bounded linear operator on a complex Hilbert space H. An operator T is called class A operator if |T 2 | ≥ |T | 2 and is called class A(k) operator if (T * |T | 2k T) 1 k+1 ≥ |T | 2 for a positive number k. In this paper, we show that σ is continuous when restricted to the set of class A(k) operators.

Research paper thumbnail of On Quasi-Class a Operators

Korean Journal of Mathematics, 2011

Let f be an analytic function defined on an open neighbourhood U of σ(T) such that f is non-const... more Let f be an analytic function defined on an open neighbourhood U of σ(T) such that f is non-constant on the connected components of U. We generalize a theorem of Sheth [10] to f (T) ∈ QA.

Research paper thumbnail of On Operators with an Absolute Value Condition

Journal of the Korean Mathematical Society, 2004

Research paper thumbnail of ON k-QUASI-CLASS A CONTRACTIONS

Korean Journal of Mathematics, 2014

A bounded linear Hilbert space operator T is said to be k-quasi-class A operator if it satisfy th... more A bounded linear Hilbert space operator T is said to be k-quasi-class A operator if it satisfy the operator inequality T * k |T 2 |T k ≥ T * k |T | 2 T k for a non-negative integer k. It is proved that if T is a k-quasi-class A contraction, then either T has a nontrivial invariant subspace or T is a proper contraction and the nonnegative operator D = T * k (|T 2 | − |T | 2)T k is strongly stable.

Research paper thumbnail of On ∗-paranormal contractions and properties for ∗-class A operators

Linear Algebra and its Applications, 2012

C .0-contraction Tensor product An operator T ∈ B(H) is called a *-class A operator if |T 2 | |T ... more C .0-contraction Tensor product An operator T ∈ B(H) is called a *-class A operator if |T 2 | |T * | 2 , and T is said to be *-paranormal if T * x 2 T 2 x for every unit vector x in H. In this paper, we show that *-paranormal contractions are the direct sum of a unitary and a C .0 completely non-unitary contraction. Also, we consider the tensor products of *-class A operators.

Research paper thumbnail of On p-quasi-hyponormal operators

Linear Algebra and its Applications, 2007

A Hilbert space operator A ∈ B(H) is said to be p-quasi-hyponormal for some 0 < p 1, A ∈ p − QH ,... more A Hilbert space operator A ∈ B(H) is said to be p-quasi-hyponormal for some 0 < p 1, A ∈ p − QH , if A * (|A| 2p − |A * | 2p)A 0. If H is infinite dimensional, then operators A ∈ p − QH are not supercyclic. Restricting ourselves to those A ∈ p − QH for which A −1 (0) ⊆ A * −1 (0), A ∈ p * − QH , a necessary and sufficient condition for the adjoint of a pure p * − QH operator to be supercyclic is proved. Operators in p * − QH satisfy Bishop's property (β). Each A ∈ p * − QH has the finite ascent property and the quasinilpotent part H 0 (A − λI) of A equals (A − λI) −1 (0) for all complex numbers λ; hence f (A) satisfies Weyl's theorem, and f (A *) satisfies a-Weyl's theorem, for all non-constant functions f which are analytic on a neighborhood of σ (A). It is proved that a Putnam-Fuglede type commutativity theorem holds for operators in p * − QH .

Research paper thumbnail of On quasi-class contractions

Linear Algebra and its Applications, 2012

Let QA denote the class of bounded linear Hilbert space operators T which satisfy the operator in... more Let QA denote the class of bounded linear Hilbert space operators T which satisfy the operator inequality T * |T 2 |T ≥ T * |T| 2 T. It is proved that if T ∈ QA is a contraction, then either T has a nontrivial invariant subspace or T is a proper contraction and the nonnegative operator D = T * (|T 2 | − |T| 2)T is strongly stable. It is shown that if T ∈ QA is a contraction with Hilbert-Schmidt defect operator such that T −1 (0) ⊆ T * −1 (0), then T is completely non-normal if and only if T ∈ C 10 , and a commutativity theorem is proved for contractions T ∈ QA. Let T u and T c denote the unitary part and the cnu part of a contraction T, respectively. We prove that if A = A u ⊕ A c and B = B u ⊕ B c are QA-contractions such that μ A c < ∞, then A and B are quasi-similar if and only A u and B u are unitarily equivalent and A c and B c are quasi-similar.

Research paper thumbnail of Continuity of the spectrum on a class of upper triangular operator matrices

Journal of Mathematical Analysis and Applications, 2010

It is proved that the set theoretic function σ , the spectrum, is continuous on the set C(i) ⊂ B(... more It is proved that the set theoretic function σ , the spectrum, is continuous on the set C(i) ⊂ B(H i) of operators A for which σ (A) = {0} implies A is nilpotent (possibly, the 0 operator) and A • = λ X 0 B (A • −λ) −1 (0) {(A • −λ) −1 (0)} ⊥ at every non-zero λ ∈ σ p (A •) for some operators X and B such that λ / ∈ σ p (B) and σ (A •) = {λ} ∪ σ (B). If C S (m) denotes the set of upper triangular operator matrices A = (A ij) m i, j=1 ∈ B(n i=1 H i), where A ii ∈ C(i) and A ii has SVEP for all 1 i m, then σ is continuous on C S (m). It is observed that a considerably large number of the more commonly considered classes of Hilbert space operators constitute sets C(i) and have SVEP.

Research paper thumbnail of Generalized Browder's and Weyl's theorems for left and right multiplication operators

Journal of Mathematical Analysis and Applications, 2010

The main objective of this work is to study generalized Browder's and Weyl's theorems for the mul... more The main objective of this work is to study generalized Browder's and Weyl's theorems for the multiplication operators L A and R B and for the elementary operator τ AB = L A R B .

Research paper thumbnail of Weyl's Theorem for Operator Matrices and the Single Valued Extension Property

Glasgow Mathematical Journal, 2006