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Displaying similar documents to “Denting point in the space of operator-valued continuous maps.”

On positive operator-valued continuous maps

Ryszard Grzaślewicz (1996)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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.

On weakly infinite-dimensional subspuees

P. Borst (1992)

Fundamenta Mathematicae

Similarity:

We will construct weakly infinite-dimensional (in the sense of Y. Smirnov) spaces X and Y such that Y contains X topologically and d i m Y = ω 0 and d i m X = ω 0 + 1 . Consequently, the subspace theorem does not hold for the transfinite dimension dim for weakly infinite-dimensional spaces.