| Title:
|
Criteria for weak compactness of vector-valued integration maps (English) |
| Author:
|
Okada, S. |
| Author:
|
Ricker, W. J. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
3 |
| Year:
|
1994 |
| Pages:
|
485-495 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Criteria are given for determining the weak compactness, or otherwise, of the integration map associated with a vector measure. For instance, the space of integrable functions of a weakly compact integration map is necessarily normable for the mean convergence topology. Results are presented which relate weak compactness of the integration map with the property of being a bicontinuous isomorphism onto its range. Finally, a detailed description is given of the compactness properties for the integration maps of a class of measures taking their values in $\ell^1$, equipped with various weak topologies. (English) |
| Keyword:
|
weakly compact integration map |
| Keyword:
|
factorization of a vector measure |
| MSC:
|
28B05 |
| MSC:
|
46A05 |
| MSC:
|
46E30 |
| MSC:
|
46G10 |
| MSC:
|
47B07 |
| MSC:
|
47B38 |
| idZBL:
|
Zbl 0805.46040 |
| idMR:
|
MR1307275 |
| . |
| Date available:
|
2009-01-08T18:12:41Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118688 |
| . |
| Reference:
|
[1] Aliprantis C.D., Burkinshaw O.: Positive Operators.Academic Press, New York, 1985. Zbl 1098.47001, MR 0809372 |
| Reference:
|
[2] Diestel J., Uhl J.J. Jr.: Vector measures.Math. Surveys, No.15, Amer. Math. Soc., Providence, 1977. Zbl 0521.46035, MR 0453964 |
| Reference:
|
[3] Dodds P.G., Ricker W.J.: Spectral measures and the Bade reflexivity theorem.J. Funct. Anal. 61 (1985), 136-163. Zbl 0577.46043, MR 0786620 |
| Reference:
|
[4] Kluvánek I., Knowles G.: Vector measures and control systems.North Holland, Amsterdam, 1976. MR 0499068 |
| Reference:
|
[5] Okada S., Ricker W.J.: Compactness properties of the integration map associated with a vector measure.Colloq. Math., to appear. Zbl 0884.28008, MR 1268062 |
| Reference:
|
[6] Okada S., Ricker W.J.: Compactness properties of vector-valued integration maps in locally convex spaces.Colloq. Math., to appear. Zbl 0821.46057, MR 1292938 |
| Reference:
|
[7] Ricker W.J.: Spectral measures, boundedly $\sigma$-complete Boolean algebras and applications to operator theory.Trans. Amer. Math. Soc. 304 (1987), 819-838. Zbl 0642.47029, MR 0911097 |
| Reference:
|
[8] Treves F.: Topological Vector Spaces, Distributions and Kernels.Academic Press, New York, 1967. Zbl 1111.46001, MR 0225131 |
| . |
