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  • Ap in Lp

    Rights statement: This is the author’s version of a work that was accepted for publication in Journal of Mathematical Analysis and Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Mathematical Analysis and Applications, 455, 1, 2017 DOI: 10.1016/j.jmaa.2017.05.075

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The parabolic algebra on Lp spaces

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>1/11/2017
<mark>Journal</mark>Journal of Mathematical Analysis and Applications
Issue number1
Volume455
Number of pages16
Pages (from-to)698-713
Publication StatusPublished
Early online date12/06/17
<mark>Original language</mark>English

Abstract

The parabolic algebra was introduced by Katavolos and Power, in 1997, as the SOT-closed operator algebra acting on L2(R) that is generated by the translation and multiplication semigroups. In particular, they proved that this algebra is reflexive and is equal to the Fourier binest algebra, that is, to the algebra of operators that leave invariant the subspaces in the Volterra nest and its analytic counterpart. We prove that a similar result holds for the corresponding algebras acting on Lp(R) , where . In the last section, it is also shown that the reflexive closures of the Fourier binests on Lp(R) are all order isomorphic for 1 < p < ∞ .

Bibliographic note

This is the author’s version of a work that was accepted for publication in Journal of Mathematical Analysis and Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Mathematical Analysis and Applications, 455, 1, 2017 DOI: 10.1016/j.jmaa.2017.05.075