Segal Bargmann空间上的循环复合算子

IF 0.3 Q4 MATHEMATICS Concrete Operators Pub Date : 2020-11-27 DOI:10.1515/conop-2022-0133

G. Ramesh, B. S. Ranjan, D. Naidu

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摘要

摘要我们研究了Segal Bargmann空间上复合算子C的循环、超循环和超循环性质ℋ(ℰ), 其中ξ（z）=Az+b，A是上的有界线性算子ℰ, b∈ℰ 其中||A||⩽1和A*b属于（I–A*A）½的范围。具体来说，在符号ξ上的一些条件下，我们证明了如果Cξ是循环的，那么A*是循环的但反过来不必成立。我们还证明了如果Cξ*是循环的，那么A是循环的。进一步证明了在空间上不存在超循环复合算子ℋ(ℰ) 对于特定类别的符号。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Cyclic Composition operators on Segal-Bargmann space

Abstract We study the cyclic, supercyclic and hypercyclic properties of a composition operator Cϕ on the Segal-Bargmann space ℋ(ℰ), where ϕ(z) = Az + b, A is a bounded linear operator on ℰ, b ∈ ℰ with ||A|| ⩽ 1 and A*b belongs to the range of (I – A*A)½. Specifically, under some conditions on the symbol ϕ we show that if Cϕ is cyclic then A* is cyclic but the converse need not be true. We also show that if Cϕ* is cyclic then A is cyclic. Further we show that there is no supercyclic composition operator on the space ℋ(ℰ) for certain class of symbols ϕ.

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