Displaying similar documents to “Type and cotype numbers of operators on Banach spaces”

On subspaces of Banach spaces where every functional has a unique norm-preserving extension

Eve Oja, Märt Põldvere (1996)

Studia Mathematica

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Let X be a Banach space and Y a closed subspace. We obtain simple geometric characterizations of Phelps' property U for Y in X (that every continuous linear functional g ∈ Y* has a unique norm-preserving extension f ∈ X*), which do not use the dual space X*. This enables us to give an intrinsic geometric characterization of preduals of strictly convex spaces close to the Beauzamy-Maurey-Lima-Uttersrud criterion of smoothness. This also enables us to prove that the U-property of the subspace...

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.

Ideals of finite rank operators, intersection properties of balls, and the approximation property

Åsvald Lima, Eve Oja (1999)

Studia Mathematica

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We characterize the approximation property of Banach spaces and their dual spaces by the position of finite rank operators in the space of compact operators. In particular, we show that a Banach space E has the approximation property if and only if for all closed subspaces F of c 0 , the space ℱ(F,E) of finite rank operators from F to E has the n-intersection property in the corresponding space K(F,E) of compact operators for all n, or equivalently, ℱ(F,E) is an ideal in K(F,E). ...

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...

Near smoothness of Banach spaces.

Józef Banas, Kishin Sadarangani (1995)

Collectanea Mathematica

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The aim of this paper is to discuss the concept of near smoothness in some Banach sequence spaces.

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.