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On positive operator-valued continuous maps

Ryszard Grzaślewicz — 1996

Commentationes Mathematicae Universitatis Carolinae

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 , ( H ) ) = { + 1 { k 0 } 𝐱 𝐱 : 𝐱 𝐒 ( H ) , k 0 is an isolated point of K } ext 𝐁 + ( C ( K , ( H ) ) ) = s-ext 𝐁 + ( C ( K , ( H ) ) ) = { f C ( K , ( H ) : f ( K ) ext 𝐁 + ( ( H ) ) } . Moreover we describe exposed, strongly exposed and denting points.

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