Geometric characterizations of the Radon-Nikodym property in Banach spaces

Huff, Robert; Morris, Peter D.

doi:10.4064/sm-56-2-157-164

Cited by 22 publications

(11 citation statements)

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“…This allows us to give an alternate proof of a result of Huff and Morris [4] concerning the density of strongly exposing functionals and to observe that weak*-Asplund spaces enjoy some of the permanence properties that Asplund spaces do. Proof.…”

mentioning

confidence: 91%

The dual of a space with the Radon-Nikodým property

Collier¹

1976

Pacific J. Math.

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mentioning

confidence: 91%

The dual of a space with the Radon-Nikodým property

Collier¹

1976

Pacific J. Math.

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“…The proof of our result is based on the following theorem which goes back to Huff and Morris [14] (see also [11] for a more general version): a set D is dentable if and only if it has open slices whose Kuratowski index of non-compactness is arbitrarily small. Let us recall that the Kuratowski index of non-compactness of a set D ⊂ X is given by…”

Section: Characterisations Of Dentabilitymentioning

confidence: 99%

Maps with the Radon–Nikodým Property

García-Lirola

Raja

2017

Set-Valued Var. Anal

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Abstract. We study dentable maps from a closed convex subset of a Banach space into a metric space as an attempt of generalize the Radon-Nikodým property to a "less linear" frame. We note that a certain part of the theory can be developed in rather great generality. Indeed, we establish that the elements of the dual which are "strongly slicing" for a given uniformly continuous dentable function form a dense G δ subset of the dual. As a consequence, the space of uniformly continuous dentable maps from a closed convex bounded set to a Banach space is a Banach space. However some interesting applications, as Stegall's variational principle, are no longer true beyond the usual hypotheses, sending us back to the classical case. Moreover, we study the connection between dentability and approximation by delta-convex functions for uniformly continuous functions. Finally, we show that the dentability of a set is closely related with the dentability of delta-convex maps defined on it.

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“…A Banach space has the RNP if and only if it does not contain a bush [3, page 216]. The reader who is interested in further historical information should see [1], [2], [3], and [5]. There are many other characterizations of the RNP discussed in [1], [2], and [3].…”

Section: Jementioning

confidence: 99%

Neighborly bushes and the Radon-Nikodým property for Banach spaces

McCartney¹

1980

Pacific J. Math.

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Geometric characterizations of the Radon-Nikodym property in Banach spaces

Cited by 22 publications

References 0 publications

The dual of a space with the Radon-Nikodým property

The dual of a space with the Radon-Nikodým property

Maps with the Radon–Nikodým Property

Neighborly bushes and the Radon-Nikodým property for Banach spaces

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