(E,F)-multipliers and applications

2012/04/12 by Fedor Sukochev, Sukochev, Fedor, Anna Tomskova +1
Mathematics · #Advanced Banach Space Theory #Advanced Topics in Algebra #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.1204.2623

openalex publication_date 2012/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For two given symmetric sequence spaces E and F we study the (E,F)-multiplier space, that is the space all of matrices M for which the Schur product M∗ A maps E into F boundedly whenever A does. We obtain several results asserting continuous embedding of (E,F)-multiplier space into the classical (p,q)-multiplier space (that is when E=l_p, F=l_q). Furthermore, we present many examples of symmetric sequence spaces E and F whose projective and injective tensor products are not isomorphic to any subspace of a Banach space with an unconditional basis, extending classical results of S. Kwapień and A. Pełczyński and of G. Bennett for the case when E=l_p, F=l_q.

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