Bochner algebras and their compact multipliers

Bochner algebras and their compact multipliers

Department of Mathematics, Uinversity of Isfahan, Isfahan, Iran

Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 841546-83111, Iran
School of Mathematics, Institute for Research in Fundamental Sciences (IPM), PO Box: 19395-5746, Tehran, Iran

Department of Mathematics, Uinversity of Isfahan, Isfahan, Iran

Abstract

Let 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, A ) to be an algebra with pointwise multiplication. Under this condition, we then characterize compact and weakly compact left multipliers on L ¹(Ω, A ).

Keywords: Arens product, compact operator, multiplier, ℓ 1-algebra, locally compact space, L 1-space, Radon measure.

MSC: Primary 28B05, Secondary 46H05, 47B48, 47B07

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Bochner algebras and their compact multipliers