The parabolic algebra on LP spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:455

Article

Kastis, E.¹ 

[1] Univ Lancaster, Dept Math Stats, Lancaster LA1 4YF, England

关键词: Operator algebra;    Nest algebra;    Reflexivity;    Binest;   

DOI  :  10.1016/j.jmaa.2017.05.075

来源: Elsevier

【 摘 要 】

The parabolic algebra was introduced by Katavolos and Power, in 1997, as the SOT closed operator algebra acting on L-2(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 L-P(R), where 1 < p < infinity. In the last section, it is also shown that the reflexive closures of the Fourier binests on L-P(R) are all order isomorphic for 1 < p < infinity. (C) 2017 Published by Elsevier Inc.

【 授权许可】

Free