Strictly cyclic algebra of operators acting on Banach spaces $H^p(\beta)$

Title:

Strictly cyclic algebra of operators acting on Banach spaces $H^p(\beta)$

Creator:

Yousefi, Bahmann

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:03417b65-3710-403b-ae8d-cef69e163e76
uuid:03417b65-3710-403b-ae8d-cef69e163e76

Subject:

the Banach space of formal power series associated with a sequence $\beta $, bounded point evaluation, strictly cyclic maximal ideal space, Schatten $p$-class, reflexive algebra, semisimple algebra, and composition operator

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let $\lbrace \beta (n)\rbrace ^{\infty }_{n=0}$ be a sequence of positive numbers and $1 \le p < \infty $. We consider the space $H^{p}(\beta )$ of all power series $f(z)=\sum ^{\infty }_{n=0}\hat{f}(n)z^{n}$ such that $\sum ^{\infty }_{n=0}|\hat{f}(n)|^{p}\beta (n)^{p} < \infty $. We investigate strict cyclicity of $H^{\infty }_{p}(\beta )$, the weakly closed algebra generated by the operator of multiplication by $z$ acting on $H^{p}(\beta )$, and determine the maximal ideal space, the dual space and the reflexivity of the algebra $H^{\infty }_{p}(\beta )$. We also give a necessary condition for a composition operator to be bounded on $H^{p}(\beta )$ when $H^{\infty }_{p}(\beta )$ is strictly cyclic.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

261-266

Source:

Czechoslovak Mathematical Journal | 2004 Volume:54 | Number:1

Harvested from:

CDK

Metadata only:

false