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BY-NC-ND 3.0 license Open Access Published by De Gruyter May 6, 2012

Bochner algebras and their compact multipliers

  • Fatemeh Abtahi EMAIL logo , Rasoul Isfahani and Ali Rejali
From the journal Mathematica Slovaca

Abstract

Let $\mathfrak{A}$ be a normed algebra with identity, Ω be a locally compact Hausdorf space and λ be a positive Radon measure on Ω with supp(λ) = Ω. In this paper, we establish a necessary and sufficient condition for L 1(Ω, $\mathfrak{A}$) to be an algebra with pointwise multiplication. Under this condition, we then characterize compact and weakly compact left multipliers on L 1(Ω, $\mathfrak{A}$).

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Published Online: 2012-5-6
Published in Print: 2012-6-1

© 2012 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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