Displaying similar documents to “Mittag-Leffler methods in analysis.”

Extension and splitting theorems for Fréchet spaces of type 2.

A. Defant, P. Domanski, M. Mastylo (1999)

Revista Matemática Complutense

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We prove the following common generalization of Maurey's extension theorem and Vogt's (DN)-(Omega) splitting theorem for Fréchet spaces: if T is an operator from a subspace E of a Fréchet space G of type 2 to a Fréchet space F of dual type 2, then T extends to a map from G into F'' whenever G/E satisfies (DN) and F satisfies (Omega).

Localization of bounded sets in tensor products.

A. Peris, M. J. Rivera (1996)

Revista Matemática de la Universidad Complutense de Madrid

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The problem of topologies of Grothendieck is considered for complete tensor products of Fréchet spaces endowed with the topology defined by an arbitrary tensor norm. Some consequences on the stability of certain locally convex properties in spaces of operators are also given.

The density condition in projective tensor products.

Wolf-Dieter Heinrichs (1999)

Revista Matemática Complutense

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In this paper we modify a construction due to J. Taskinen to get a Fréchet space F which satisfies the density condition such that the complete injective tensor product l2 x~eF'b does not satisfy the strong dual density condition of Bierstedt and Bonet. In this way a question that remained open in Heinrichs (1997) is solved.

The density condition and the strong dual density condition by operator.

Wolf-Dieter Heinrichs (1997)

Collectanea Mathematica

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The aim of the present article is to introduce and investigate topological properties by operator. We obtain good stability properties for the density condition and the strong dual density condition by taking injective tensor products. Further we analyze the connection to (DF)-properties by operator.

Multiplicative characterization of Hilbert spaces and other interesting classes of Banach spaces.

A. Rodríguez Palacios (1996)

Revista Matemática de la Universidad Complutense de Madrid

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For a Banach space X, we show how the existence of a norm-one element u in X and a norm-one continuous bilinear mapping f: X x X --> X satisfying f(x,u) = f(u,x) = x for all x in X, together with some more intrinsic conditions, can be utilized to characterize X as a member of some relevant subclass of the class of Banach spaces.

On invariant elements for positive operators.

R. Zaharopol (1997)

Revista Matemática de la Universidad Complutense de Madrid

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In the paper we study the existence of nonzero positive invariant elements for positive operators in Riesz spaces. The class of Riesz spaces for which the results are valid is large enough to contain all the Banach lattices with order continuous norms. All the results obtained in earlier works deal with positive operators in KB-spaces and in many of them the approach is based upon the use of Banach limits. The methods created for KB-spaces cannot be extended to our more general setting;...