| Title:
|
Strictly cyclic algebra of operators acting on Banach spaces $H^p(\beta)$ (English) |
| Author:
|
Yousefi, B. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
54 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
261-266 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
the Banach space of formal power series associated with a sequence $\beta $ |
| Keyword:
|
bounded point evaluation |
| Keyword:
|
strictly cyclic maximal ideal space |
| Keyword:
|
Schatten $p$-class |
| Keyword:
|
reflexive algebra |
| Keyword:
|
semisimple algebra |
| Keyword:
|
composition operator |
| MSC:
|
46E15 |
| MSC:
|
47A16 |
| MSC:
|
47A25 |
| MSC:
|
47B37 |
| idZBL:
|
Zbl 1049.47033 |
| idMR:
|
MR2040238 |
| . |
| Date available:
|
2009-09-24T11:12:06Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127883 |
| . |
| Reference:
|
[1] J. B. Conway: A Course in Functional Analysis.Springer-Verlag, New York, 1985. Zbl 0558.46001, MR 0768926 |
| Reference:
|
[2] J. B. Conway: The Theory of Subnormal Operators.American Mathematical Society, 1991. Zbl 0743.47012, MR 1112128 |
| Reference:
|
[3] K. Seddighi, K. Hedayatiyan and B. Yousefi: Operators acting on certain Banach spaces of analytic functions.Internat. J. Math. Sci. 18 (1995), 107–110. MR 1311579, 10.1155/S0161171295000147 |
| Reference:
|
[4] A. L. Shields: Weighted shift operators and analytic function theory.Math. Survey, A.M.S. Providence 13 (1974), 49–128. Zbl 0303.47021, MR 0361899 |
| Reference:
|
[5] B. Yousefi: On the space $\ell ^{p}(\beta )$.Rend. Circ. Mat. Palermo Serie II XLIX (2000), 115–120. MR 1753456 |
| Reference:
|
[6] B. Yousefi: Bounded analytic structure of the Banach space of formal power series.Rend. Circ. Mat. Palermo Serie II LI (2002), 403–410. MR 1947463 |
| . |
