有界对称区域上Dirichlet空间中的紧Toeplitz算子

陈建军, 王晓峰, 夏锦

数学学报 ›› 2015, Vol. 58 ›› Issue (6) : 923-934.

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数学学报 ›› 2015, Vol. 58 ›› Issue (6) : 923-934. DOI: 10.12386/A2015sxxb0091
论文

有界对称区域上Dirichlet空间中的紧Toeplitz算子

    陈建军1, 王晓峰2, 夏锦2
作者信息 +

Compact Toeplitz Operators on Dirichlet Space of Bounded Symmetric Domains

    Jian Jun CHEN1, Xiao Feng WANG2, Jin XIA2
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文章历史 +

摘要

介绍了有界对称区域Ω上Dirichlet空间中的Toeplitz算子的紧性:如果S是有限个 Toeplitz算子乘积的有限和,S是紧算子当且仅当S的Berezin变换(z)趋于0.

Abstract

We study the compactness of Toeplitz operators on bounded symmetric domains Ω. Then we will obtain the result that if S equals a finite sum of finite products of Toeplitz operators on Dirichlet space, then S is compact if and only if its Berezin transformation (z) → 0 as z → ∂Ω.

关键词

Toeplitz算子 / Berezin变换 / Dirichlet空间 / 紧算子

Key words

Toeplitz operator / Berezin transform / Dirichlet space / compact operator

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陈建军, 王晓峰, 夏锦. 有界对称区域上Dirichlet空间中的紧Toeplitz算子. 数学学报, 2015, 58(6): 923-934 https://doi.org/10.12386/A2015sxxb0091
Jian Jun CHEN, Xiao Feng WANG, Jin XIA. Compact Toeplitz Operators on Dirichlet Space of Bounded Symmetric Domains. Acta Mathematica Sinica, Chinese Series, 2015, 58(6): 923-934 https://doi.org/10.12386/A2015sxxb0091

参考文献

[1] Axler S., Zheng D., Compact operators via the Berezin transform, Indiana Univ. Math. J., 1998, 47(2): 387–400.

[2] Cartan E., Sur les domaines bornés homogènes de l'espace de n variables complexes, Abh. Math. Sem, Univ. Hamburg, 1935, 11: 116–162.

[3] Engliš M., Compact Toeplitz operators via the Berezin transform on bounded symmetric domains, Integr. Equ. Oper. Theory, 1999, 33: 426–455.

[4] Engliš M., Erratum to “Compact Toeplitz operators via the Berezin transform on bounded symmetric domains”, Integr. Equ. Oper. Theory, 1999, 34: 500–501.

[5] Faraut J., Koranyi A., Function spaces and Repreducing kernels on bounded symmetric domains, J. Funct. Anal., 1990, 88: 64–89.

[6] Koranyi A., Anaylytic invariants of bounded symmetric domains, Proc. Amer. Math. Soc., 1968, 19: 279– 284.

[7] Koranyi A., Complex Analysis and Symmetric Domains, Ecole CIMPA-Universite de Poitiers, Poitiers, 1988.

[8] Nomura T., Algebraically independent generators of invariant differential operators on a symmetric cone, J. Reine Angew. Math., 1989, 400: 122–133.

[9] Xia J., Wang X. F., Cao G. F., Compact operators on Dirichlet space, Acta Math. Sci., Ser. A, 2009, 29A(5): 1196–1205.

[10] Yan Z. M., Duality and differential operators on the Bergman spaces of bounded symmetric domains, J. Funct. Anal., 1992, 105: 171–186.

[11] Zhu K. H., Holomorphic Besov spaces on bounded symmetric domains, Quart. J. Math. Oxford, 1995, 46: 239–256.

[12] Zhu K. H., Holomorphic Besov spaces on bounded symmetric domains II, Indiana Univ. Math. J., 1995, 44: 1017–1031.

[13] Zhu K. H., Spaces of Holomorphic Functions in the Unit Ball, Graduate Text in Mathematics Series 226, Springer, 2010.

基金

国家自然科学基金资助项目(11471084,11301101);广州市教育局科技计划项目(2012A018)

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