Displaying similar documents to “Solution to a problem of S. Rolewicz”

A subsequence characterization of sequences spanning isomorphically polyhedral Banach spaces

G. Androulakis (1998)

Studia Mathematica

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Let (x_n) be a sequence in a Banach space X which does not converge in norm, and let E be an isomorphically precisely norming set for X such that (*) ∑_n |x*(x_{n+1} - x_n)| < ∞, ∀x* ∈ E. Then there exists a subsequence of (x_n) which spans an isomorphically polyhedral Banach space. It follows immediately from results of V. Fonf that the converse is also true: If Y is a separable isomorphically polyhedral Banach space then there exists a normalized M-basis (x_n) which spans Y and...

Separable quotients of Banach spaces.

Jorge Mújica (1997)

Revista Matemática de la Universidad Complutense de Madrid

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In this survey we show that the separable quotient problem for Banach spaces is equivalent to several other problems for Banach space theory. We give also several partial solutions to the problem.

Effective constructions of separable quotients of Banach spaces.

Marek Wójtowicz (1997)

Collectanea Mathematica

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A simple way of obtaining separable quotients in the class of weakly countably determined (WCD) Banach spaces is presented. A large class of Banach lattices, possessing as a quotient c0, l1, l2, or a reflexive Banach space with an unconditional Schauder basis, is indicated.

On l^∞ subspaces of Banach spaces.

Patrick N. Dowling (2000)

Collectanea Mathematica

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We obtain refinement of a result of Partington on Banach spaces containing isomorphic copies of l-∞. Motivated by this result, we prove that Banach spaces containing asymptotically isometric copies of l-∞ must contain isometric copies of l-∞.

Answer to a question by M. Feder about K(X,Y).

G. Emmanuele (1993)

Revista Matemática de la Universidad Complutense de Madrid

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We show that a Banach space constructed by Bourgain-Delbaen in 1980 answers a question put by Feder in 1982 about spaces of compact operators.