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Keywords:
exposed point; denting point; Hilbert space; positive operator
exposed point; denting point; Hilbert space; positive operator
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.
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