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Haagerup tensor products and Schur multipliers
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In this paper we compare various classes of Schur multipliers: classical matrix Schur multipliers, discrete Schur multipliers, Schur multipliers with respect to measures and Schur multipliers with respect to spectral measures. The main result says that in the case of Schur multipliers with respect to measures and spectral measures such Schur multipliers coincide isometrically with the Haagerup tensor products of the corresponding
L
∞
L^\infty
spaces. We deduce this result from a well-known analogue of it for discrete Schur multipliers.
American Mathematical Society (AMS)
Title: Haagerup tensor products and Schur multipliers
Description:
In this paper we compare various classes of Schur multipliers: classical matrix Schur multipliers, discrete Schur multipliers, Schur multipliers with respect to measures and Schur multipliers with respect to spectral measures.
The main result says that in the case of Schur multipliers with respect to measures and spectral measures such Schur multipliers coincide isometrically with the Haagerup tensor products of the corresponding
L
∞
L^\infty
spaces.
We deduce this result from a well-known analogue of it for discrete Schur multipliers.
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