Unconditionality, Fourier multipliers and Schur multipliers

Details Unconditionality, Fourier multipliers and Schur multipliers Unconditionality, Fourier multipliers and Schur multipliers

2011-11-07

arxiv.org/abs/1111.1664v7

Mathematics

Functional Analysis

minor corrections; 17 pages ; to appear in Colloquium Mathematicum

Scientific paper

Let $G$ be an infinite locally compact abelian group. If $X$ is Banach space, we show that if every bounded Fourier multiplier $T$ on $L^2(G)$ has the property that $T\ot Id_X$ is bounded on $L^2(G,X)$ then the Banach space $X$ is isomorphic to a Hilbert space. Moreover, if $1

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