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SEQUENCES OF POWERS OF toeplitz operatorS ON THE BERGMAN SPACE

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Acta Mathematica Scientia 2021年第3期41卷 657-669页

作者： Yong CHEN Kei Ji IZUCHI Kou Hei IZUCHI Young Joo LEE Department of Mathematics Hangzhou Normal UniversityHangzhou 311121China Department of Mathematics Niigata UniversityNiigata 950-2181Japan Department of Mathematics Faculty of EducationYamaguchi UniversityYamaguchi 753-8511Japan Department of Mathematics Chonnam National UniversityGwangju 61186Korea

We consider toeplitz operators Tu with symbol u on the Bergman space of the unit ball,and then study the convergences and summability for the sequences of powers of toeplitz *** first charactreize analytic symbolsφfor which the sequence Tφ*kf or Tφkf converges to 0 or∞as k→∞in norm for every nonzero Bergman function ***,we characterize analytic symbolsφfor which the norm of such a sequence is summable or not *** also study the corresponding problems on an infinite direct sum of Bergman spaces as a generalization of our result.

关键词： Bergman space toeplitz operator

Commutators and Semi-commutators of Monomial toeplitz operators on the Pluriharmonic Hardy Space

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Chinese Annals of Mathematics,Series B 2020年第5期41卷 717-732页

作者： Yingying ZHANG Xingtang DONG School of Mathematics Tianjin UniversityTianjin 300354China

In this paper,the authors completely characterize the finite rank commutator and semi-commutator of two monomial toeplitz operators on the pluriharmonic Hardy space of the torus or the unit *** a consequence,many non-... 详细信息

关键词： toeplitz operator Pluriharmonic Hardy space Commutator Semi-commutator Monomial symbol

toeplitz operators with Unbounded Symbols on Segal-Bargmann Space

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Journal of Mathematical Research with Applications 2015年第3期35卷 237-255页

作者： Li HE Guangfu CAO Department of Mathematics Guangzhou University

In this paper,we construct a function φ in L2(Cn,d Vα) which is unbounded on any neighborhood of each point in Cnsuch that Tφ is a trace class operator on the SegalBargmann space H2(Cn,d Vα).In addition,we also ch... 详细信息

关键词： Segal-Bargmann space toeplitz operator unbounded function Schatten class

Product of toeplitz operators on the Harmonic Dirichlet Space

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Acta Mathematica Sinica,English Series 2012年第5期28卷 1033-1040页

作者： Lian Kuo ZHAO School of Mathematics and Computer Science Shanxi Normal University

In this paper, we study toeplitz operators with harmonic symbols on the harmonic Dirichlet space, and show that the product of two toeplitz operators is another toeplitz operator only if one factor is constant.

关键词： Harmonic Dirichlet space toeplitz operator zero product

Commutant of Analytic toeplitz operators on the Bergman Space

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Acta Mathematica Sinica,English Series 2010年第12期26卷 2255-2258页

作者： Jia Yi JIANG Di Sheng XU Department of Mathematics, Peking University, Beijing 100871, P.R. China Department of Mathematics Peking University Beijing P. R. China

In this paper, we characterize the commutant of toeplitz operators on weighted Bergman space with symbol polynomial by using algebraic curves theory.

关键词： toeplitz operator commutant Bergman space algebraic curves

toeplitz operators and Algebras on Dirichlet Spaces

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Communications in Mathematical Research 1999年第1期 1-4页

作者： Cao Guangfu (Department of Mathematics, Sichuan University, Chengdu, 610064) Sun Shanli

ＬｅｔＤｂｅｔｈｅｕｎｉｔｄｉｓｋｉｎｔｈｅｃｏｍｐｌｅｘｐｌａｎｅＣ，ａｎｄｄＡ（ｚ）＝１πｄｘｄｙｔｈｅｎｏｒｍａｌｉｚｅｄＬｅｂｅｓｇｕｅｍｅａｓｕｒｅｏｎＤ．ＴｈｅＳｏｂｏｌｅｖｓｐａｃｅＬ２，１ｉｓｄｅｆｉ... 详细信息

ＬｅｔＤｂｅｔｈｅｕｎｉｔｄｉｓｋｉｎｔｈｅｃｏｍｐｌｅｘｐｌａｎｅＣ，ａｎｄｄＡ（ｚ）＝１πｄｘｄｙｔｈｅｎｏｒｍａｌｉｚｅｄＬｅｂｅｓｇｕｅｍｅａｓｕｒｅｏｎＤ．ＴｈｅＳｏｂｏｌｅｖｓｐａｃｅＬ２，１ｉｓｄｅｆｉｎｅｄｔｏｂｅｔｈｅｃｏｌｅｃｔｉ...

关键词： Dirichlet Space toeplitz operator toeplitz Algebra

Hyponormal toeplitz operators on the Polydisk

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Acta Mathematica Sinica,English Series 2012年第2期28卷 333-348页

作者： Yu Feng LU Yan Yue SHI School of Mathematical Sciences Dalian University of TechnologyDalian 116024P.R.China

By bounded vector-valued functions and block matrix representations of Hankel operators, we completely characterize the hyponormality of toeplitz operators on the Hardy space of the polydisk.

关键词： Hyponormality toeplitz operator Hankel operator polydisk block matrix representation

ON　CONNECTIVITY　OF　THE　ESSENTIAL　SPECTRA　OF　toeplitz　operatorS　WITH　SYMBOLS　IN　H∞＋C

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Chinese Annals of Mathematics,Series B 1995年第1期16卷 93-102页

作者： CAO GUANGFU SUN SHANLI(Department of Mathematics, Jinn University Changchun 130023, China.) JILIN UNIV DEPT MATHCHANGCHUN 130023PEOPLES R CHINA

This paper discusses the connectivity of the essential spectra of toeplitz operators with symbols in H∞ +C on Hardy spaces and weighted Bergman spaces for several complex variables.

关键词： Hardy space Weighted Bergman space toeplitz operator Essential spectrum.

Algebraic Properties of toeplitz operators on the Harmonic Bergman Space

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Journal of Mathematical Research with Applications 2016年第4期36卷 495-504页

作者： Jingyu YANG Yufeng LU Xiaoying WANG School of Mathematics and Statistics Chifeng University Department of Mathematics Dalian University of Technology

In this paper, we first investigate the finite-rank product problem of several toeplitz operators with quasihomogeneous symbols on the harmonic Bergman space. Next, we characterize finite rank commutators and semi-com... 详细信息

关键词： toeplitz operator Harmonic Bergman space quasihomogeneous commutator finite rank