The parabolic algebra on Lp spaces

Kastis, Eleftherios Michail (2017) The parabolic algebra on Lp spaces. Journal of Mathematical Analysis and Applications, 455 (1). pp. 698-713. ISSN 0022-247X

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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 < ∞ .

Item Type:
Journal Article
Journal or Publication Title:
Journal of Mathematical Analysis and Applications
Additional Information:
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
Uncontrolled Keywords:
?? operator algebranest algebrareflexivitybinestanalysisapplied mathematics ??
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Deposited On:
06 Mar 2018 14:10
Last Modified:
31 Dec 2023 00:55