Multipliers and equivalence of functions, spaces, and operators

IF 1.1 2区 数学 Q1 MATHEMATICS
M. C. Câmara, C. Carteiro, W. T. Ross
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引用次数: 0

Abstract

By interpreting the well-known Brown–Halmos theorem for Toeplitz operators in terms of multipliers, we formulate a Brown–Halmos analogue for the product of generalized Toeplitz operators, defined as compressions of multiplication operators to closed subspaces of \(L^2({\mathbb {T}})\). We use this to define equivalences between two operators in that class by means of multipliers between the spaces where they act. Necessary and sufficient conditions for such an equivalence to be unitary or a similarity are established. The results are applied to Toeplitz and Hankel operators, truncated Toeplitz operators, and dual truncated Toeplitz operators.

函数、空间和算子的乘法和等价性
通过用乘数解释著名的托普利兹算子布朗-哈尔莫斯定理,我们提出了广义托普利兹算子乘积的布朗-哈尔莫斯类似定理,它被定义为乘法算子对 \(L^2({\mathbb {T}})/) 的封闭子空间的压缩。我们利用这一点来定义该类中两个算子之间的等价关系,即它们作用的空间之间的乘数关系。我们建立了这种等价性是单一性或相似性的必要条件和充分条件。这些结果适用于托普利兹和汉克尔算子、截断托普利兹算子和对偶截断托普利兹算子。
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来源期刊
CiteScore
2.00
自引率
8.30%
发文量
67
审稿时长
>12 weeks
期刊介绍: The Banach Journal of Mathematical Analysis (Banach J. Math. Anal.) is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Banach J. Math. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and operator theory and all modern related topics. Banach J. Math. Anal. normally publishes survey articles and original research papers numbering 15 pages or more in the journal’s style. Shorter papers may be submitted to the Annals of Functional Analysis or Advances in Operator Theory.
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