Denting point in the space of operator-valued continuous maps.

Ryszard Grzaslewicz; Samir B. Hadid

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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 $ext-ray C_{+} (K, ℒ (H)) = {ℝ_{+} 1_{{k_{0}}} 𝐱 \otimes 𝐱 : 𝐱 \in 𝐒 (H), k_{0} is an isolated point of K}$ $ext 𝐁_{+} (C (K, ℒ (H))) = s-ext 𝐁_{+} (C (K, ℒ (H))) = {f \in C (K, ℒ (H) : f (K) \subset ext 𝐁_{+} (ℒ (H))}$ . Moreover we describe exposed, strongly exposed and denting points.

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