Orlicz Algebras Associated to a Banach Function Space

Author:

CHEN Chung-chuan1ORCID,BAGHERİ SALEC Ali Reza2ORCID,TABATABAİE Seyed Mohammad2ORCID

Affiliation:

1. National Taichung University of Education

2. University of Qom

Abstract

In this paper, we study the spaces ${\mathcal X}^\Phi$ as Banach algebras, where $\mathcal X$ is a quasi-Banach space and $\Phi$ is a Young function, and extend some well-known facts regarding Lebesgue and Orlicz spaces on this new structure. Also, for each $p\geq 1$, we give some necessary condition for the space $\mathcal{X}^p$ to be a Banach algebra under the pointwise product.

Publisher

Hacettepe University

Subject

Geometry and Topology,Statistics and Probability,Algebra and Number Theory,Analysis

Reference25 articles.

1. A.R. Bagheri Salec and S.M. Tabatabaie, {\it Some necessary and sufficient conditions for convolution weighted Orlicz algebras}, Bull. Iranian Math. Soc. (to appear)

2. A.R. Bagheri Salec, S. Ivkovic and S.M. Tabatabaie, \emph{Spaceability on some classes of Banach spaces}, submitted.

3. A.R. Bagheri Salec, V. Kumar and S.M. Tabatabaie, {\it Convolution properties of Orlicz spaces on hypergroups}, Proc. Amer. Math. Soc. (to appear)

4. L. Bernal-Gonz\'alez and M.O. Cabrera, \emph{Spaceability of strict order integrability}, J. Math. Anal. Appl. {\bf 385} (2012) 303--309.

5. R. del Campo, A. Fern\'andez, F. Mayoral and F. Naranjo, \emph{Orlicz spaces associated to a quasi-Banach function space. Applications to vector measures and interpolation}, Collect. Math. (2020). https://doi.org/10.1007/s13348-020-00295-1

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