| Title:
|
On positive operator-valued continuous maps (English) |
| Author:
|
Grzaślewicz, Ryszard |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
3 |
| Year:
|
1996 |
| Pages:
|
499-505 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper the geometric properties of the positive cone and positive part of the unit ball of the space of operator-valued continuous space are discussed. In particular we show that $\text{ext-ray} \text{C}_+(K,\mathcal L(H)) = \{\Bbb R_+ {\bold 1}_{\{k_0\}} \bold x\otimes\bold x : \bold x\in \bold S(H), k_0 \text{ is an isolated point of } K\}$ $\text{ext} \bold B_+(\text{C}(K,\mathcal L(H))) = \text{s-ext } \bold B_+(\text{C}(K,\mathcal L(H)))=\{f\in \text{C}(K,\mathcal L(H) : f(K)\subset \text{ext } \bold B_+(\mathcal L(H))\}$. Moreover we describe exposed, strongly exposed and denting points. (English) |
| Keyword:
|
exposed point |
| Keyword:
|
denting point |
| Keyword:
|
Hilbert space |
| Keyword:
|
positive operator |
| MSC:
|
46B20 |
| MSC:
|
46B28 |
| MSC:
|
46E40 |
| MSC:
|
47A56 |
| MSC:
|
47D20 |
| MSC:
|
47L07 |
| idZBL:
|
Zbl 0881.47001 |
| idMR:
|
MR1426914 |
| . |
| Date available:
|
2009-01-08T18:25:38Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118856 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
