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- W2014513600 abstract "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." @default.
- W2014513600 created "2016-06-24" @default.
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- W2014513600 date "2011-09-19" @default.
- W2014513600 modified "2023-10-04" @default.
- W2014513600 title "The controlled separable projection property for Banach spaces" @default.
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- W2014513600 doi "https://doi.org/10.2478/s11533-011-0096-x" @default.
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