Abstract: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
$ext-ray C_+(K,\Cal L(H)) = \{\Bbb R_+ {\bold 1}_{\{k_0\}} \bold x\otimes \bold x : \bold x\in \bold S(H), k_0 is an isolated point of K\}$
$ext \bold B_+(C(K,\Cal L(H))) = s-ext \bold B_+(C(K,\Cal L(H)))$
$=\{f\in C(K,\Cal L(H) : f(K)\subset ext \bold B_+(\Cal L(H))\}$.
Moreover we describe exposed, strongly exposed and denting points.
Keywords: exposed point, denting point, Hilbert space, positive operator
AMS Subject Classification: Primary 47D20; Secondary 46B20