| Title:
|
Convolution operators on the dual of hypergroup algebras (English) |
| Author:
|
Ghaffari, Ali |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
44 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
669-679 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be a hypergroup. In this paper, we define a locally convex topology $\beta $ on $L(X)$ such that $(L(X),\beta )^*$ with the strong topology can be identified with a Banach subspace of $L(X)^*$. We prove that if $X$ has a Haar measure, then the dual to this subspace is $L_C(X)^{**}= \operatorname{cl}\{F\in L(X)^{**}; F$ has compact carrier\}. Moreover, we study the operators on $L(X)^*$ and $L_0^\infty(X)$ which commute with translations and convolutions. We prove, among other things, that if $\operatorname{wap}(L(X))$ is left stationary, then there is a weakly compact operator $T$ on $L(X)^*$ which commutes with convolutions if and only if $L(X)^{**}$ has a topologically left invariant functional. For the most part, $X$ is a hypergroup not necessarily with an involution and Haar measure except when explicitly stated. (English) |
| Keyword:
|
Arens regular |
| Keyword:
|
hypergroup algebra |
| Keyword:
|
weakly almost periodic |
| Keyword:
|
convolution operators |
| MSC:
|
43A10 |
| MSC:
|
43A62 |
| MSC:
|
46H99 |
| idZBL:
|
Zbl 1098.43001 |
| idMR:
|
MR2062883 |
| . |
| Date available:
|
2009-01-08T19:32:03Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119421 |
| . |
| Reference:
|
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| . |
