Dechao Zheng - Academia.edu (original) (raw)

Papers by Dechao Zheng

Research paper thumbnail of Finite rank commutators and semicommutators of Toeplitz operators with harmonic symbols

Illinois Journal of Mathematics, 2007

In this paper we completely characterize finite rank semicommutator or commutator of two Toeplitz... more In this paper we completely characterize finite rank semicommutator or commutator of two Toeplitz operators with bounded harmonic symbols on the Bergman space. We show that if the product of two Toeplitz operators with bounded harmonic symbols has finite rank, then one of the Toeplitz operators must be zero.

Research paper thumbnail of The semi-commutator of Toeplitz operators on the bidisc

In this paper we characterize when the semi-commutator TfTg−TfgT_fT_g-T_{fg}TfTg−Tfg of two Toeplitz operators ... more In this paper we characterize when the semi-commutator TfTg−TfgT_fT_g-T_{fg}TfTg−Tfg of two Toeplitz operators TfT_fTf and TgT_gTg on the Hardy space of the bidisc is zero. We also show that there is no nonzero finite rank semi-commutator on the bidisc. Furthermore explicit examples of compact semi-commutators with symbols continuous on the bitorus T2T^2T2 are given.

Research paper thumbnail of COMPOSITION OPERATORS WITH CLOSED RANGE ON THE BLOCH SPACE

In this note we investigate conditions under which a holomorphic self-map of the unit disk induce... more In this note we investigate conditions under which a holomorphic self-map of the unit disk induces a composition operator with closed range on the Bloch space.

Research paper thumbnail of ALGEBRAIC AND SPECTRAL PROPERTIES OF DUAL TOEPLITZ OPERATORS

Dual Toeplitz operators on the orthogonal complement of the Bergman space are dened to be multipl... more Dual Toeplitz operators on the orthogonal complement of the Bergman space are dened to be multiplication operators followed by pro- jection onto the orthogonal complement. In this paper we study algebraic and spectral properties of dual Toeplitz operators.

Research paper thumbnail of Products of Block Toeplitz operators

In this paper we characterize when the product of two block Toeplitz operators is a compact pertu... more In this paper we characterize when the product of two block Toeplitz operators is a compact perturbation of a block Toeplitz operator on the Hardy space of the open unit disk. Necessary and sufficient conditions are given for the commutator of two block Toeplitz operators to be compact.

Research paper thumbnail of ISOLATED POINTS AND ESSENTIAL COMPONENTS OF COMPOSITION OPERATORS ON H1

We consider the topological space of all composition operators on the Banach algebra of bounded a... more We consider the topological space of all composition operators on the Banach algebra of bounded analytic functions on the unit disk. We obtain a function theoretic characterization of isolated points and show that each isolated composition operator is essentially isolated.

Research paper thumbnail of Standard deviation and Schatten class Hankel operators on the Segal-Bargmann space

Indiana University Mathematics Journal, 2004

ABSTRACT. We consider Hankel operators on the Segal-Bargmann spaceH,aÑBn;dvÖ .

Research paper thumbnail of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi></mrow><annotation encoding="application/x-tex">m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">m</span></span></span></span>-Berezin transform and compact operators

Revista Matemática Iberoamericana, 2000

Research paper thumbnail of Compact composition operators on BMOA and the Bloch space

Proceedings of the American Mathematical Society, 2009

Research paper thumbnail of Essentially commuting Toeplitz operators

Pacific Journal of Mathematics, 1999

(0.4) Conversely, Halmos (15) has shown that if Tf commutes with Tg, then one of Conditions 0.2, ... more (0.4) Conversely, Halmos (15) has shown that if Tf commutes with Tg, then one of Conditions 0.2, 0.3 and 0.4 holds, i.e., f2 H1 and g2 H1 or f2 H1 and g2 H1 or af +bg = c (0.5)

Research paper thumbnail of Products of Bergman space Toeplitz operators on the polydisk

Mathematische Annalen, 2006

Research paper thumbnail of The Berezin Transform on the Toeplitz Algebra

This paper studies the boundary behavior of the Berezin transform on the C*-algebra generated by ... more This paper studies the boundary behavior of the Berezin transform on the C*-algebra generated by the analytic Toeplitz operators on the Bergman space.

Research paper thumbnail of Bounded Toeplitz products on Bergman spaces of the unit ball

Journal of Mathematical Analysis and Applications, 2007

ABSTRACT We consider the question for which square integrable analytic functions f and g on the u... more ABSTRACT We consider the question for which square integrable analytic functions f and g on the unit ball the densely defined products are bounded on the weighted Bergman spaces. We prove results analogous to those we obtained in the setting of the unit disk and the polydisk.

Research paper thumbnail of Bounded Toeplitz products on the Bergman space of the polydisk

Journal of Mathematical Analysis and Applications, 2003

ABSTRACT We consider the question for which square integrable analytic functions f and g on the p... more ABSTRACT We consider the question for which square integrable analytic functions f and g on the polydisk the densely defined products T f T ¯ g are bounded on the Bergman space. We prove results analogous to those we obtained in the setting of the unit disk [K. Stroethoff, D. Zheng, J. Funct. Anal. 169 (1999) 289–313].  2003 Elsevier Science (USA). All rights reserved.

Research paper thumbnail of Toeplitz algebra and Hankel algebra on the harmonic Bergman space

Journal of Mathematical Analysis and Applications, 2002

In this paper we completely characterize compact Toeplitz operators on the harmonic Bergman space... more In this paper we completely characterize compact Toeplitz operators on the harmonic Bergman space. By using this result we establish the short exact sequences associated with the Toeplitz algebra and the Hankel algebra. We show that the Fredholm index of each Fredholm operator in the Toeplitz algebra or the Hankel algebra is zero.

Research paper thumbnail of Products of Hankel and Toeplitz Operators on the Bergman Space

Journal of Functional Analysis, 1999

ABSTRACT We consider the question for which square integrable analytic functions f and g on the u... more ABSTRACT We consider the question for which square integrable analytic functions f and g on the unit disk the densely defined products TfTg are bounded on the Bergman space. We prove results analogous to those obtained by the second author [17] for such Toeplitz products on the Hardy space. We furthermore obtain similar results for Hankel products HfH*g, where f and g are square integrable on the unit disk, and for the mixed Haplitz products HfTg and TgH*f, where f and g are square integrable on the unit disk and g is analytic.

Research paper thumbnail of The distribution function inequality for a finite sum of finite products of Toeplitz operators

Journal of Functional Analysis, 2005

Research paper thumbnail of Essentially commuting Hankel and Toeplitz operators

Journal of Functional Analysis, 2003

Research paper thumbnail of Toeplitz algebras on the disk

Journal of Functional Analysis, 2007

Research paper thumbnail of Invariant Subspaces, Quasi-invariant Subspaces, and Hankel Operators

Journal of Functional Analysis, 2001

In this paper, using the theory of Hilbert modules we study invariant subspaces of the Bergman sp... more In this paper, using the theory of Hilbert modules we study invariant subspaces of the Bergman spaces on bounded symmetric domains and quasi-invariant subspaces of the Segal–Bargmann spaces. We completely characterize small Hankel operators with finite rank on these spaces.

Research paper thumbnail of Finite rank commutators and semicommutators of Toeplitz operators with harmonic symbols

Illinois Journal of Mathematics, 2007

In this paper we completely characterize finite rank semicommutator or commutator of two Toeplitz... more In this paper we completely characterize finite rank semicommutator or commutator of two Toeplitz operators with bounded harmonic symbols on the Bergman space. We show that if the product of two Toeplitz operators with bounded harmonic symbols has finite rank, then one of the Toeplitz operators must be zero.

Research paper thumbnail of The semi-commutator of Toeplitz operators on the bidisc

In this paper we characterize when the semi-commutator TfTg−TfgT_fT_g-T_{fg}TfTg−Tfg of two Toeplitz operators ... more In this paper we characterize when the semi-commutator TfTg−TfgT_fT_g-T_{fg}TfTg−Tfg of two Toeplitz operators TfT_fTf and TgT_gTg on the Hardy space of the bidisc is zero. We also show that there is no nonzero finite rank semi-commutator on the bidisc. Furthermore explicit examples of compact semi-commutators with symbols continuous on the bitorus T2T^2T2 are given.

Research paper thumbnail of COMPOSITION OPERATORS WITH CLOSED RANGE ON THE BLOCH SPACE

In this note we investigate conditions under which a holomorphic self-map of the unit disk induce... more In this note we investigate conditions under which a holomorphic self-map of the unit disk induces a composition operator with closed range on the Bloch space.

Research paper thumbnail of ALGEBRAIC AND SPECTRAL PROPERTIES OF DUAL TOEPLITZ OPERATORS

Dual Toeplitz operators on the orthogonal complement of the Bergman space are dened to be multipl... more Dual Toeplitz operators on the orthogonal complement of the Bergman space are dened to be multiplication operators followed by pro- jection onto the orthogonal complement. In this paper we study algebraic and spectral properties of dual Toeplitz operators.

Research paper thumbnail of Products of Block Toeplitz operators

In this paper we characterize when the product of two block Toeplitz operators is a compact pertu... more In this paper we characterize when the product of two block Toeplitz operators is a compact perturbation of a block Toeplitz operator on the Hardy space of the open unit disk. Necessary and sufficient conditions are given for the commutator of two block Toeplitz operators to be compact.

Research paper thumbnail of ISOLATED POINTS AND ESSENTIAL COMPONENTS OF COMPOSITION OPERATORS ON H1

We consider the topological space of all composition operators on the Banach algebra of bounded a... more We consider the topological space of all composition operators on the Banach algebra of bounded analytic functions on the unit disk. We obtain a function theoretic characterization of isolated points and show that each isolated composition operator is essentially isolated.

Research paper thumbnail of Standard deviation and Schatten class Hankel operators on the Segal-Bargmann space

Indiana University Mathematics Journal, 2004

ABSTRACT. We consider Hankel operators on the Segal-Bargmann spaceH,aÑBn;dvÖ .

Research paper thumbnail of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi></mrow><annotation encoding="application/x-tex">m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">m</span></span></span></span>-Berezin transform and compact operators

Revista Matemática Iberoamericana, 2000

Research paper thumbnail of Compact composition operators on BMOA and the Bloch space

Proceedings of the American Mathematical Society, 2009

Research paper thumbnail of Essentially commuting Toeplitz operators

Pacific Journal of Mathematics, 1999

(0.4) Conversely, Halmos (15) has shown that if Tf commutes with Tg, then one of Conditions 0.2, ... more (0.4) Conversely, Halmos (15) has shown that if Tf commutes with Tg, then one of Conditions 0.2, 0.3 and 0.4 holds, i.e., f2 H1 and g2 H1 or f2 H1 and g2 H1 or af +bg = c (0.5)

Research paper thumbnail of Products of Bergman space Toeplitz operators on the polydisk

Mathematische Annalen, 2006

Research paper thumbnail of The Berezin Transform on the Toeplitz Algebra

This paper studies the boundary behavior of the Berezin transform on the C*-algebra generated by ... more This paper studies the boundary behavior of the Berezin transform on the C*-algebra generated by the analytic Toeplitz operators on the Bergman space.

Research paper thumbnail of Bounded Toeplitz products on Bergman spaces of the unit ball

Journal of Mathematical Analysis and Applications, 2007

ABSTRACT We consider the question for which square integrable analytic functions f and g on the u... more ABSTRACT We consider the question for which square integrable analytic functions f and g on the unit ball the densely defined products are bounded on the weighted Bergman spaces. We prove results analogous to those we obtained in the setting of the unit disk and the polydisk.

Research paper thumbnail of Bounded Toeplitz products on the Bergman space of the polydisk

Journal of Mathematical Analysis and Applications, 2003

ABSTRACT We consider the question for which square integrable analytic functions f and g on the p... more ABSTRACT We consider the question for which square integrable analytic functions f and g on the polydisk the densely defined products T f T ¯ g are bounded on the Bergman space. We prove results analogous to those we obtained in the setting of the unit disk [K. Stroethoff, D. Zheng, J. Funct. Anal. 169 (1999) 289–313].  2003 Elsevier Science (USA). All rights reserved.

Research paper thumbnail of Toeplitz algebra and Hankel algebra on the harmonic Bergman space

Journal of Mathematical Analysis and Applications, 2002

In this paper we completely characterize compact Toeplitz operators on the harmonic Bergman space... more In this paper we completely characterize compact Toeplitz operators on the harmonic Bergman space. By using this result we establish the short exact sequences associated with the Toeplitz algebra and the Hankel algebra. We show that the Fredholm index of each Fredholm operator in the Toeplitz algebra or the Hankel algebra is zero.

Research paper thumbnail of Products of Hankel and Toeplitz Operators on the Bergman Space

Journal of Functional Analysis, 1999

ABSTRACT We consider the question for which square integrable analytic functions f and g on the u... more ABSTRACT We consider the question for which square integrable analytic functions f and g on the unit disk the densely defined products TfTg are bounded on the Bergman space. We prove results analogous to those obtained by the second author [17] for such Toeplitz products on the Hardy space. We furthermore obtain similar results for Hankel products HfH*g, where f and g are square integrable on the unit disk, and for the mixed Haplitz products HfTg and TgH*f, where f and g are square integrable on the unit disk and g is analytic.

Research paper thumbnail of The distribution function inequality for a finite sum of finite products of Toeplitz operators

Journal of Functional Analysis, 2005

Research paper thumbnail of Essentially commuting Hankel and Toeplitz operators

Journal of Functional Analysis, 2003

Research paper thumbnail of Toeplitz algebras on the disk

Journal of Functional Analysis, 2007

Research paper thumbnail of Invariant Subspaces, Quasi-invariant Subspaces, and Hankel Operators

Journal of Functional Analysis, 2001

In this paper, using the theory of Hilbert modules we study invariant subspaces of the Bergman sp... more In this paper, using the theory of Hilbert modules we study invariant subspaces of the Bergman spaces on bounded symmetric domains and quasi-invariant subspaces of the Segal–Bargmann spaces. We completely characterize small Hankel operators with finite rank on these spaces.