Geodesic
On positive operator-valued continuous maps
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 3, pp. 499-505

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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.
Classification : 46B20, 46B28, 46E40, 47A56, 47D20, 47L07
Keywords: exposed point; denting point; Hilbert space; positive operator 
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     author = {Grza\'slewicz, Ryszard},
     title = {On positive operator-valued continuous maps},
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     pages = {499--505},
     publisher = {mathdoc},
     volume = {37},
     number = {3},
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     zbl = {0881.47001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1996__37_3_a6/}
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Grzaślewicz, Ryszard. On positive operator-valued continuous maps. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 3, pp. 499-505. http://geodesic.mathdoc.fr/item/CMUC_1996__37_3_a6/