Research Highlights

On multipliers and compact multipliers of commutative semigroup algebra ℓp(S,ω)

Authors :- Prakash A. Dabhi & Darshana B. Likhada

Publication :- Advances in Operator Theory, volume 7, Article number: 4 (2022)

Let 1<p<∞, and let q be the conjugate index of p. Let ω be a uniform weight on an abelian semigroup S satisfying ω−q⋆ω−q≤ω−q, and let A be a commutative Banach algebra with approximate identity bounded by 1. We shall determine the multiplier algebra of ℓp(S,ω,A) under some conditions. We apply this result to characterize some compact multipliers on ℓp(S,ω) when S is cancellative. A necessary and sufficient condition for the semisimplicity of ℓp(S,ω) is also discussed.