Radial Toeplitz Operators on the Fock Space and Square-Root-Slowly Oscillating Sequences

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• 作者：Kevin Esmeral ; Egor A. Maximenko
• 关键词：Toeplitz operator ; Radial ; Fock space ; Slowly oscillating sequence
• 刊名：Complex Analysis and Operator Theory
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：10
• 期：7
• 页码：1655-1677
• 全文大小：749 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Operator Theory
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1661-8262
• 卷排序：10

文摘

In this paper we show that the C*-algebra generated by radial Toeplitz operators with \(L_{\infty }\)-symbols acting on the Fock space is isometrically isomorphic to the C*-algebra of bounded sequences uniformly continuous with respect to the square-root-metric \(\rho (j,k)=|\sqrt{j}-\sqrt{k}\,|\). More precisely, we prove that the sequences of eigenvalues of radial Toeplitz operators form a dense subset of the latter C*-algebra of sequences.