Cyclic Composition operators on Segal-Bargmann space

• Published in: Concrete operators (Warsaw, Poland) Vol. 9; no. 1; pp. 127 - 138
• Main Authors: Ramesh, G., Ranjan, B. Sudip, Naidu, D. Venku
• Format: Journal Article
• Language: English
• Published: De Gruyter 01-01-2022
• Subjects: composition operator; Cyclic operator; hypercyclic and supercyclic operators; Primary 47B33; reproducing kernel Hilbert space; Secondary 46E22, 47A16; Segal-Bargmann space
• ISSN: 2299-3282; 2299-3282
• DOI: 10.1515/conop-2022-0133

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