Displaying similar documents to “Prediction sequences in smooth Banach spaces”

Vector series whose lacunary subseries converge

Lech Drewnowski, Iwo Labuda (2000)

Studia Mathematica

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The area of research of this paper goes back to a 1930 result of H. Auerbach showing that a scalar series is (absolutely) convergent if all its zero-density subseries converge. A series ∑ n x n in a topological vector space X is called ℒ-convergent if each of its lacunary subseries ∑ k x n k (i.e. those with n k + 1 - n k → ∞ ) converges. The space X is said to have the Lacunary Convergence Property, or LCP, if every ℒ-convergent series in X is convergent; in fact, it is then subseries convergent. The Zero-Density...

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...

Lacunary convergence of series in L revisited.

Lech Drewnowski (2000)

Revista Matemática Complutense

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A simpler proof is given for the recent result of I. Labuda and the author that a series in the space L (lambda) is subseries convergent if each of its lacunary subseries converges.

Tightness, integral equicontinuity and compactness for evolution problems in Banach spaces

Riccarda Rossi, Giuseppe Savaré (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Compactness in the space L p ( 0 , T ; B ) , B being a separable Banach space, has been deeply investigated by J.P. Aubin (1963), J.L. Lions (1961, 1969), J. Simon (1987), and, more recently, by J.M. Rakotoson and R. Temam (2001), who have provided various criteria for relative compactness, which turn out to be crucial tools in the existence proof of solutions to several abstract time dependent problems related to evolutionary PDEs. In the present paper, the problem is examined in view of Young measure...