Taiwanese Journal of Mathematics

ON CYCLICITY IN THE SPACE $H^{p}(\beta)$

K. Hedayatian

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Abstract

Let $\{\beta(n)\}$ be a sequence of positive numbers with $\beta(0) = 1$ and let $p\gt 0$. By the space $H^{p}(\beta)$, we mean the set of all formal power series $\sum^{\infty}_{n=0} \hat{f}(n) z^{n}$ for which $\sum^{\infty}_{n=0} |\hat{f}(n)|^{p} \beta(n)^{p} \lt \infty$. In this paper, we study cyclic vectors for the forward shift operator and supercyclic vectors for the backward shift operator on the space $H^{p} (\beta)$.

Article information

Source
Taiwanese J. Math., Volume 8, Number 3 (2004), 429-442.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500407663

Digital Object Identifier
doi:10.11650/twjm/1500407663

Mathematical Reviews number (MathSciNet)
MR2163316

Zentralblatt MATH identifier
1079.47012

Subjects
Primary: 47A16: Cyclic vectors, hypercyclic and chaotic operators 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)

Keywords
cyclicity supercyclicity $H^{p}(\beta)$ polynomial shift

Citation

Hedayatian, K. ON CYCLICITY IN THE SPACE $H^{p}(\beta)$. Taiwanese J. Math. 8 (2004), no. 3, 429--442. doi:10.11650/twjm/1500407663. https://projecteuclid.org/euclid.twjm/1500407663


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