Jagjit Singh - Profile on Academia.edu (original) (raw)
Address: Tokyo, Tokyo, Japan
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Papers by Jagjit Singh
arXiv (Cornell University), Nov 1, 2014
Assuming a unitarily invariant norm ||| • ||| is given on a two-sided ideal of bounded linear ope... more Assuming a unitarily invariant norm ||| • ||| is given on a two-sided ideal of bounded linear operators acting on a separable Hilbert space, it induces some unitarily invariant norms ||| • ||| on matrix algebras M n for all finite values of n via |||A||| = |||A ⊕ 0|||. We show that if A is a C *-algebra of finite dimension k and Φ : A → M n is a unital completely positive map, then |||Φ(AB) − Φ(A)Φ(B)||| ≤ 1 4 |||I n ||| |||I kn |||d A d B for any A, B ∈ A , where d X denotes the diameter of the unitary orbit {U XU * : U is unitary} of X and I m stands for the identity of M m. Further we get an analogous inequality for certain n-positive maps in the setting of full matrix algebras by using some matrix tricks. We also give a Grüss operator inequality in the setting of C *-algebras of arbitrary dimension and apply it to some inequalities involving continuous fields of operators.
Linear Algebra and its Applications, 2012
We present an operator version of the Callebaut inequality involving the interpolation paths and ... more We present an operator version of the Callebaut inequality involving the interpolation paths and apply it to the weighted operator geometric means. We also establish a matrix version of the Callebaut inequality and as a consequence obtain an inequality including the Hadamard product of matrices.
Linear Algebra and its Applications, 2011
We present a weak majorization inequality and apply it to prove eigenvalue and unitarily invarian... more We present a weak majorization inequality and apply it to prove eigenvalue and unitarily invariant norm extensions of a version of the Bohr's inequality due to Vasić and Kečkić.
The purpose of this note is to prove Hadamard product versions of the Chebyshev and the Kantorovi... more The purpose of this note is to prove Hadamard product versions of the Chebyshev and the Kantorovich inequalities for positive real numbers. We also prove a generalization of Fiedler's inequality.
Gruess inequality for some types of positive linear maps
Journal of Operator Theory, 2015
ABSTRACT
The purpose of this note is to prove Hadamard product versions of the Chebyshev and the Kantorovi... more The purpose of this note is to prove Hadamard product versions of the Chebyshev and the Kantorovich inequalities for positive real numbers. We also prove a generalization of Fiedler's inequality.
arXiv (Cornell University), Nov 1, 2014
Assuming a unitarily invariant norm ||| • ||| is given on a two-sided ideal of bounded linear ope... more Assuming a unitarily invariant norm ||| • ||| is given on a two-sided ideal of bounded linear operators acting on a separable Hilbert space, it induces some unitarily invariant norms ||| • ||| on matrix algebras M n for all finite values of n via |||A||| = |||A ⊕ 0|||. We show that if A is a C *-algebra of finite dimension k and Φ : A → M n is a unital completely positive map, then |||Φ(AB) − Φ(A)Φ(B)||| ≤ 1 4 |||I n ||| |||I kn |||d A d B for any A, B ∈ A , where d X denotes the diameter of the unitary orbit {U XU * : U is unitary} of X and I m stands for the identity of M m. Further we get an analogous inequality for certain n-positive maps in the setting of full matrix algebras by using some matrix tricks. We also give a Grüss operator inequality in the setting of C *-algebras of arbitrary dimension and apply it to some inequalities involving continuous fields of operators.
Linear Algebra and its Applications, 2012
We present an operator version of the Callebaut inequality involving the interpolation paths and ... more We present an operator version of the Callebaut inequality involving the interpolation paths and apply it to the weighted operator geometric means. We also establish a matrix version of the Callebaut inequality and as a consequence obtain an inequality including the Hadamard product of matrices.
Linear Algebra and its Applications, 2011
We present a weak majorization inequality and apply it to prove eigenvalue and unitarily invarian... more We present a weak majorization inequality and apply it to prove eigenvalue and unitarily invariant norm extensions of a version of the Bohr's inequality due to Vasić and Kečkić.
The purpose of this note is to prove Hadamard product versions of the Chebyshev and the Kantorovi... more The purpose of this note is to prove Hadamard product versions of the Chebyshev and the Kantorovich inequalities for positive real numbers. We also prove a generalization of Fiedler's inequality.
Gruess inequality for some types of positive linear maps
Journal of Operator Theory, 2015
ABSTRACT
The purpose of this note is to prove Hadamard product versions of the Chebyshev and the Kantorovi... more The purpose of this note is to prove Hadamard product versions of the Chebyshev and the Kantorovich inequalities for positive real numbers. We also prove a generalization of Fiedler's inequality.