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    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

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The parabolic algebra on Lp spaces. / Kastis, Eleftherios Michail.
In: Journal of Mathematical Analysis and Applications, Vol. 455, No. 1, 01.11.2017, p. 698-713.

Research output: Contribution to Journal/Magazine › Journal article

Harvard

Kastis, EM 2017, 'The parabolic algebra on Lp spaces', Journal of Mathematical Analysis and Applications, vol. 455, no. 1, pp. 698-713. https://doi.org/10.1016/j.jmaa.2017.05.075

APA

Kastis, E. M. (2017). The parabolic algebra on Lp spaces. Journal of Mathematical Analysis and Applications, 455(1), 698-713. https://doi.org/10.1016/j.jmaa.2017.05.075

Vancouver

Kastis EM. The parabolic algebra on Lp spaces. Journal of Mathematical Analysis and Applications. 2017 Nov 1;455(1):698-713. Epub 2017 Jun 12. doi: 10.1016/j.jmaa.2017.05.075

Author

Kastis, Eleftherios Michail. / The parabolic algebra on Lp spaces. In: Journal of Mathematical Analysis and Applications. 2017 ; Vol. 455, No. 1. pp. 698-713.

Bibtex

@article{49353cd2c71a44369bcc2bcc780c8d2f,
title = "The parabolic algebra on Lp spaces",
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 < ∞ .",
keywords = "Operator algebra, Nest algebra, Reflexivity, Binest",
author = "Kastis, {Eleftherios Michail}",
note = "This is the author{\textquoteright}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",
year = "2017",
month = nov,
day = "1",
doi = "10.1016/j.jmaa.2017.05.075",
language = "English",
volume = "455",
pages = "698--713",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "1",

}

RIS

TY - JOUR

T1 - The parabolic algebra on Lp spaces

AU - Kastis, Eleftherios Michail

N1 - 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

PY - 2017/11/1

Y1 - 2017/11/1

N2 - 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 < ∞ .

AB - 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 < ∞ .

KW - Operator algebra

KW - Nest algebra

KW - Reflexivity

KW - Binest

U2 - 10.1016/j.jmaa.2017.05.075

DO - 10.1016/j.jmaa.2017.05.075

M3 - Journal article

VL - 455

SP - 698

EP - 713

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -