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May 2018 Convolution-continuous bilinear operators acting on Hilbert spaces of integrable functions
Ezgi Erdoğan, José M. Calabuig, Enrique A. Sánchez Pérez
Ann. Funct. Anal. 9(2): 166-179 (May 2018). DOI: 10.1215/20088752-2017-0034

Abstract

We study bilinear operators acting on a product of Hilbert spaces of integrable functions—zero-valued for couples of functions whose convolution equals zero—that we call convolution-continuous bilinear maps. We prove a factorization theorem for them, showing that they factor through 1. We also present some applications for the case when the range space has some relevant properties, such as the Orlicz or Schur properties. We prove that 1 is the only Banach space for which there is a norming bilinear map which equals zero exactly in those couples of functions whose convolution is zero. We also show some examples and applications to generalized convolutions.

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Ezgi Erdoğan. José M. Calabuig. Enrique A. Sánchez Pérez. "Convolution-continuous bilinear operators acting on Hilbert spaces of integrable functions." Ann. Funct. Anal. 9 (2) 166 - 179, May 2018. https://doi.org/10.1215/20088752-2017-0034

Information

Received: 9 January 2017; Accepted: 2 March 2017; Published: May 2018
First available in Project Euclid: 6 December 2017

zbMATH: 06873694
MathSciNet: MR3795082
Digital Object Identifier: 10.1215/20088752-2017-0034

Subjects:
Primary: 47H60‎
Secondary: 43A25 , 46G25

Keywords: bilinear operator , convolution , factorization , Fourier transform , summability

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.9 • No. 2 • May 2018
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