| Title:
|
Projections from $L(X,Y)$ onto $K(X,Y)$ (English) |
| Author:
|
John, Kamil |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
4 |
| Year:
|
2000 |
| Pages:
|
765-771 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Generalization of certain results in [Sap] and simplification of the proofs are given. We observe e.g.: Let $X$ and $Y$ be Banach spaces such that $X$ is weakly compactly generated Asplund space and $X^*$ has the approximation property (respectively $Y$ is weakly compactly generated Asplund space and $Y^*$ has the approximation property). Suppose that $L(X,Y)\neq K(X,Y)$ and let $1<\lambda<2$. Then $X$ (respectively $Y$) can be equivalently renormed so that any projection $P$ of $L(X,Y)$ onto $K(X,Y)$ has the sup-norm greater or equal to $\lambda $. (English) |
| Keyword:
|
compact operator |
| Keyword:
|
approximation property |
| Keyword:
|
reflexive Banach space |
| Keyword:
|
projection |
| Keyword:
|
separability |
| MSC:
|
46B28 |
| idZBL:
|
Zbl 1050.46016 |
| idMR:
|
MR1800167 |
| . |
| Date available:
|
2009-01-08T19:07:10Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119208 |
| . |
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| . |
