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

Walter Schachermayer

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Displaying similar documents to “For a Banach space isomorphic to its square the Radon-Nikodým property and the Krein-Milman property are equivalent”

The Space of Differences of Convex Functions on [0, 1]

Zippin, M. (2000)

Serdica Mathematical Journal

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∗Participant in Workshop in Linear Analysis and Probability, Texas A & M University, College Station, Texas, 2000. Research partially supported by the Edmund Landau Center for Research in Mathematical Analysis and related areas, sponsored by Minerva Foundation (Germany). The space K[0, 1] of differences of convex functions on the closed interval [0, 1] is investigated as a dual Banach space. It is proved that a continuous function f on [0, 1] belongs to K[0, 1] ...

Solution to a problem of S. Rolewicz

V. Montesinos (1985)

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A geometric characterization of the Radon-Nikodym property in Banach spaces

J. Bourgain (1978)

Compositio Mathematica

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Dentability and finite-dimensional decompositions

J. Bourgain (1980)

Studia Mathematica

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Reflexive Banach spaces without equivalent norms which are uniformly convex or uniformly differentiable in every direction

D. Kutzarova, S. Troyanski (1982)

Studia Mathematica

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Equivalent norms on separable Asplund spaces

C. Finet, W. Schachermayer (1989)

Studia Mathematica

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On Bárány's theorems of Carathéodory and Helly type

Ehrhard Behrends (2000)

Studia Mathematica

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The paper begins with a self-contained and short development of Bárány’s theorems of Carathéodory and Helly type in finite-dimensional spaces together with some new variants. In the second half the possible generalizations of these results to arbitrary Banach spaces are investigated. The Carathéodory-Bárány theorem has a counterpart in arbitrary dimensions under suitable uniform compactness or uniform boundedness conditions. The proper generalization of the Helly-Bárány theorem reads...

RNP and KMP are equivalent for some Banach spaces with shrinking basis

Ginés López, Juan Mena (1996)

Studia Mathematica

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We get a characterization of PCP in Banach spaces with shrinking basis. Also, we prove that the Radon-Nikodym and Krein-Milman properties are equivalent for closed, convex and bounded subsets of some Banach spaces with shrinking basis.

On Uniformly Convex and Uniformly Kadec-Klee Renomings

Lancien, Gilles (1995)

Serdica Mathematical Journal

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We give a new construction of uniformly convex norms with a power type modulus on super-reflexive spaces based on the notion of dentability index. Furthermore, we prove that if the Szlenk index of a Banach space is less than or equal to ω (first infinite ordinal) then there is an equivalent weak* lower semicontinuous positively homogeneous functional on X* satisfying the uniform Kadec-Klee Property for the weak*-topology (UKK*). Then we solve the UKK or UKK* renorming problems for...

RNP and KMP are incomparable properties in noncomplete spaces.

López, G. (1996)

Acta Mathematica Universitatis Comenianae. New Series

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