Effective constructions of separable quotients of Banach spaces.

Marek Wójtowicz

Displaying similar documents to “Effective constructions of separable quotients of Banach spaces.”

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.

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...

Basic sequences and smooth norms in Banach spaces

Catherine Finet (1988)

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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.

Any separable Banach space with the bounded approximation property is a complemented subspace of a Banach space with a basic

A. Pełczyński (1971)

Studia Mathematica

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Geometric properties related to the fixed point property in Banach spaces.

Helga Fetter, Berta Gamboa De Buen (2000)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

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Solution to a problem of S. Rolewicz

V. Montesinos (1985)

Studia Mathematica

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Equivalent norms on separable Asplund spaces

C. Finet, W. Schachermayer (1989)

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Banach spaces with finite dimensional expansions of identity and universal bases of finite dimensional subspaces

A. Pełczyński, P. Wojtaszczyk (1971)

Studia Mathematica

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Rotund and uniformly rotund Banach spaces.

V. Montesinos, J. R. Torregrosa (1991)

Collectanea Mathematica

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In this paper we prove that the geometrical notions of Rotundity and Uniform Rotundity of the norm in a Banach space are stable for the generalized Banach products.

Banach spaces with a supershrinking basis

Ginés López (1999)

Studia Mathematica

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We prove that a Banach space X with a supershrinking basis (a special type of shrinking basis) without $c_{0}$ copies is somewhat reflexive (every infinite-dimensional subspace contains an infinite-dimensional reflexive subspace). Furthermore, applying the $c_{0}$ -theorem by Rosenthal, it is proved that X contains order-one quasireflexive subspaces if X is not reflexive. Also, we obtain a characterization of the usual basis in $c_{0}$ .