Release Time:2019-03-13  Hits:

Indexed by: Journal Article

Date of Publication: 2019-02-01

Journal: ACTA MATHEMATICA SINICA-ENGLISH SERIES

Included Journals: Scopus、SCIE

Volume: 35

Issue: 2

Page Number: 227-238

ISSN: 1439-8516

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

Abstract: 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.