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2011 | 9 | 6 | 1252-1266

Tytuł artykułu

The controlled separable projection property for Banach spaces

Treść / Zawartość

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Języki publikacji

EN

Abstrakty

EN
Let X, Y be two Banach spaces. We say that Y is a quasi-quotient of X if there is a continuous operator R: X → Y such that its range, R(X), is dense in Y. Let X be a nonseparable Banach space, and let U, W be closed subspaces of X and Y, respectively. We prove that if X has the Controlled Separable Projection Property (CSPP) (this is a weaker notion than the WCG property) and Y is a quasi-quotient of X, then the structure of Y resembles the structure of a separable Banach space: (a) Y/W is norm-separable iff its dual W ⊥ is weak*-separable, (b) every weak*-separable subset of B Y* is weak*-metrizable, (c) every weak*-null sequence in the unit sphere of Y* contains a “nice“ subsequence; and (d) if U is separable, then X/U also has the CSPP. Property (a) yields an easy way of obtaining separable quotients in a class of Banach spaces. We also study the CSPP for C(K)-spaces, where K is a Mrówka compact space, e.g., we prove that the CSPP is not a three-space property.

Wydawca

Czasopismo

Rocznik

Tom

9

Numer

6

Strony

1252-1266

Opis fizyczny

Daty

wydano
2011-12-01
online
2011-09-23

Twórcy

  • Universidad de Valencia
  • Uniwersytet Kazimierza Wielkiego

Bibliografia

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