On positive operator-valued continuous maps
Grzaślewicz, Ryszard
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996), p. 499-505 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 1996-01-01
Classification:  46B20,  46B28,  46E40,  47A56,  47D20,  47L07 
@article{118856,
     author = {Ryszard Grza\'slewicz},
     title = {On positive operator-valued continuous maps},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {37},
     year = {1996},
     pages = {499-505},
     zbl = {0881.47001},
     mrnumber = {1426914},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118856}
}

Grzaślewicz, Ryszard. On positive operator-valued continuous maps. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) pp. 499-505. http://gdmltest.u-ga.fr/item/118856/

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