Bochner algebras and their compact multipliers

Bochner algebras and their compact multipliers

Fatemeh Abtahi

Rasoul Nasr Isfahani

Ali Rejali

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