Extreme operators on AL-spaces

A. Iwanik

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For a Banach space isomorphic to its square the Radon-Nikodým property and the Krein-Milman property are equivalent

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Ondrej F. K. Kalenda (2005)

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We study the classes of complex Banach spaces with Valdivia dual unit ball. We give complex analogues of several theorems on real spaces. Further we study relationship of these complex Banach spaces with their real versions and that of real Banach spaces and their complexification. We also formulate several open problems.

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Theorems of Krein Milman type for certain convex sets of functions operators

Robert R. Phelps (1970)

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Sufficient conditions are given in order that, for a bounded closed convex subset $B$ of a locally convex space $E$ , the set $C (X, B)$ of continuous functions from the compact space $X$ into $B$ , is the uniformly closed convex hull in $C (X, E)$ of its extreme points. Applications are made to the unit ball of bounded (or compact, or weakly compact) operators from certain Banach spaces into $C (X)$ .