Bergman空间上的斜Toeplitz算子

安恒斌;蹇人宜

数学学报 ›› 2004, Vol. 47 ›› Issue (1) : 103-110.

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数学学报 ›› 2004, Vol. 47 ›› Issue (1) : 103-110. DOI: 10.12386/A2004sxxb0015
论文

Bergman空间上的斜Toeplitz算子

    安恒斌;蹇人宜
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Slant Toeplitz Operators on Bergman Space

    Heng Bin AN(1),Ren Yi JIAN(2)
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摘要

本文讨论了Bergman空间上斜Toeplitz算子的若干性质,证明了:如果线性算子S在每个Lap(1

Abstract

In this paper, we set up some operator properties of slant Toeplitz operators on Bergman space. We prove that if S is a linear operator on every Lap (1 < p < ∞), then 5 is compact on La2 if and only if S(z), the Berezin transform of S, satisfies S(z)→0 (z→(?)D). Our main result can be used to prove that if S is a finite sum of finite products of Toeplitz operators or slant Toeplitz operators, then S is compact if and only if S(z)→0 as z→(?)D.

关键词

Berezin变换 / Toeplitz算子 / Bergman空间

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安恒斌;蹇人宜. Bergman空间上的斜Toeplitz算子. 数学学报, 2004, 47(1): 103-110 https://doi.org/10.12386/A2004sxxb0015
Heng Bin AN(1),Ren Yi JIAN(2). Slant Toeplitz Operators on Bergman Space. Acta Mathematica Sinica, Chinese Series, 2004, 47(1): 103-110 https://doi.org/10.12386/A2004sxxb0015
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