Cyclic Composition operators on Segal-Bargmann space
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 w...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2022-11-01
|
| Series: | Concrete Operators |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/conop-2022-0133 |
| Summary: | 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. |
|---|---|
| ISSN: | 2299-3282 |