Neighborly bushes and the Radon-Nikodým property for Banach spaces

McCartney, Philip W.

doi:10.2140/pjm.1980.87.157

Pacific J. Math.

1980

DOI: 10.2140/pjm.1980.87.157

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Neighborly bushes and the Radon-Nikodým property for Banach spaces

Philip W. McCartney¹

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“…Then (y*) is a tree in BY.. By the lifting property of bounded trees in dual spaces (this follows easily from a compactness argument, cf. [6]) there exists a tree (z*) in BY. such that z*(y) = y*(y) for all.y in Y0.…”

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confidence: 99%

The geometry of weak Radon-Nikodým sets in dual Banach spaces

Riddle¹

1982

Proc. Amer. Math. Soc.

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mentioning

confidence: 99%

The geometry of weak Radon-Nikodým sets in dual Banach spaces

Riddle¹

1982

Proc. Amer. Math. Soc.

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The asymptotic-norming and Radon-Nikodým properties for Banach spaces

James

1981

Ark. Mat.

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A separable Banach space with the Radon-Nikodým property that is not isomorphic to a subspace of a separable dual

McCartney¹,

O’Brien²

1980

Proc. Amer. Math. Soc.

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Abstract. In this paper an example is given of a separable Banach space with the Radon-Nikodym property that is not isomorphic to a subspace of a separable dual space.In [5] Uhl showed that if every separable closed linear subspace of a Banach space A" is isomorphic to a subspace of a separable dual, then X has the Radon-Nikodym property (RNP). In that same paper, he asked whether every separable Banach space X with the RNP is isomorphic to a subspace of a separable dual space. Three years later, in 1975, Stegall [4] showed that if X is a subspace of a dual space, then the answer to Uhl's question is yes. We present in this note an example which shows that for general Banach spaces the answer is no.

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Neighborly bushes and the Radon-Nikodým property for Banach spaces

Cited by 3 publications

References 7 publications

The geometry of weak Radon-Nikodým sets in dual Banach spaces

The geometry of weak Radon-Nikodým sets in dual Banach spaces

The asymptotic-norming and Radon-Nikodým properties for Banach spaces

A separable Banach space with the Radon-Nikodým property that is not isomorphic to a subspace of a separable dual

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