6533b86cfe1ef96bd12c82dc

RESEARCH PRODUCT

(p,q)-summing sequences

Oscar BlascoJosé Luis Arregui

subject

Discrete mathematicsSequenceFunctional analysisDual spaceApproximation propertyApplied MathematicsBanach spaceCharacterization (mathematics)BoundedCombinatoricsType and cotypeSequences in Banach spacesInterpolation spaceIntegral and (pq)-summing operatorsLp spaceGrothendieck theoremAnalysisMathematics

description

Abstract A sequence (x j ) in a Banach space X is (p,q) -summing if for any weakly q -summable sequence (x j ∗ ) in the dual space we get a p -summable sequence of scalars (x j ∗ (x j )) . We consider the spaces formed by these sequences, relating them to the theory of (p,q) -summing operators. We give a characterization of the case p=1 in terms of integral operators, and show how these spaces are relevant for a general question on Banach spaces and their duals, in connection with Grothendieck theorem.

yearjournalcountryeditionlanguage
2002-10-01Journal of Mathematical Analysis and Applications
https://doi.org/10.1016/s0022-247x(02)00379-7