On Banach spaces with the Gelfand-Phillips property

Drewnowski, Lech

doi:10.1007/bf01229808

Cited by 59 publications

(44 citation statements)

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“…If condition (2) or (3) holds, then B X * * * has a weak * -dense, weak * -CSC subset, namely B X * , from which it again follows that X * * has both the GPP and the WGP by [5] and [9]. If X is coreflexive, then X * is coreflexive, and hence every subspace of X * is coreflexive.…”

Section: Corollary Let X Be a C * -Algebra Or A Subspace Of K(h) Thmentioning

confidence: 99%

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An extension property for Banach spaces

Freedman

2002

Colloq. Math.

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Section: Corollary Let X Be a C * -Algebra Or A Subspace Of K(h) Thmentioning

confidence: 99%

“…See [9] for details on the WGP. Since the GPP and the WGP are both hereditary [5], [9], it follows that if X * * has both the GPP and the WGP, then X has the hereditary properties (G) and (L). We use this fact to prove the final result.…”

Section: Proof If X Has Property (G) or (L) We May Apply Part (D) Omentioning

confidence: 99%

An extension property for Banach spaces

Freedman

2002

Colloq. Math.

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“…The Gelfand-Phillips property has attracted considerable attention over the last twenty years, which resulted in several interesting papers, see for instance Bourgain & Diestel [5], Drewnowski [6], Schlumprecht [28], Sinha & Arora [26], Freedman [9]. The class (GP) of spaces having this property is quite wide, and includes (i) l 1 (κ) for every κ;…”

Section: Mazur Versus Gelfand-phillipsmentioning

confidence: 99%

On sequential properties of Banach spaces, spaces of measures and densities

Borodulin–Nadzieja

Plebanek

2010

Czech Math J

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We answer in negative the problem if the existence of a Pmeasure implies the existence of a P-point. Namely, we show that if we add random reals to a certain 'unique P-point' model, then in the resulting model we will have a P-measure but not P-points. Also, we investigate the question if there is a P-measure in the Silver model. We show that rapid filters cannot be extended to a P-measure in the extension by ω product of Silver forcings and that in the model obtained by the countable support ω 2 -iteration of countable product of Silver forcings there are no P-measures of countable Maharam type.

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“…Hence separable or reflexive Banach spaces are Gelfand-Phillips spaces. (See also [7] and [17].) Of course, their intrinsic properties have also been studied (see e.g.…”

Section: Pablo Galindo (Communicated By Theodore Gamelin)mentioning

confidence: 99%