SEQUENCES OF POWERS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE

• 作者: Yong CHEN Kei Ji IZUCHI Kou Hei IZUCHI Young Joo LEE
• 来源期刊: 数学物理学报（英文版）
• 年，卷（期）: 2021,（3）
• 页码范围: 657-669
• 页数: 13页
• 语种: 英文
• DOI: 10.3969/j.issn.0252-9602.2021.03.001

摘要

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 operators.We first charactreize analytic symbols ψ for which the sequence Tψ*kf or Tkψf converges to 0 or ∞ as k → ∞ in norm for every nonzero Bergman function f.Also,we characterize analytic symbols ψ for which the norm of such a sequence is summable or not summable.We also study the corresponding problems on an infinite direct sum of Bergman spaces as a generalization of our result.