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论文类型：期刊论文

发表时间：2019-02-01

发表刊物：ACTA MATHEMATICA SINICA-ENGLISH SERIES

收录刊物：SCIE、Scopus

卷号：35

期号：2

页面范围：227-238

ISSN号：1439-8516

关键字：Radial operators; (m, lambda)-Berezin transform; weighted Bergman spaces; Toeplitz operators; 47B35; 47B37; 47A58

摘要：In this paper, we study radial operators in Toeplitz algebra on the weighted Bergman spaces over the polydisk by the (m, )-Berezin transform and find that a radial operator can be approximated in norm by Toeplitz operators without any conditions. We prove that the compactness of a radial operator is equivalent to the property of vanishing of its (0, )-Berezin transform on the boundary. In addition, we show that an operator S is radial if and only if its (m, )-Berezin transform is a separately radial function.