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Strictly cyclic algebra of operators acting on Banach spaces $H^p(\beta)$
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 1, pp. 261-266 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 46E15, 47A16, 47A25, 47B37
Keywords: 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; composition operator 
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     author = {Yousefi, B.},
     title = {Strictly cyclic algebra of operators acting on {Banach} spaces $H^p(\beta)$},
     journal = {Czechoslovak Mathematical Journal},
     pages = {261--266},
     year = {2004},
     volume = {54},
     number = {1},
     mrnumber = {2040238},
     zbl = {1049.47033},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2004_54_1_a23/}
}
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Yousefi, B. Strictly cyclic algebra of operators acting on Banach spaces $H^p(\beta)$. Czechoslovak Mathematical Journal, Tome 54 (2004) no. 1, pp. 261-266. http://geodesic.mathdoc.fr/item/CMJ_2004_54_1_a23/

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