Cyclic Composition operators on Segal-Bargmann space

IF 0.3 Q4 MATHEMATICS
G. Ramesh, B. S. Ranjan, D. Naidu
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引用次数: 0

Abstract

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.
Segal Bargmann空间上的循环复合算子
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。
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来源期刊
Concrete Operators
Concrete Operators MATHEMATICS-
CiteScore
1.00
自引率
16.70%
发文量
10
审稿时长
22 weeks
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