Multipliers and Relative Completion in Weighted Lorentz Spaces

Abstract

Let G be a locally compact Abelian group with Haar measure μ. In the present paper, first the authors discussed some properties of weighted Lorentz space. Then they defined the relative completion Ā of a subspace A of the weighted Lorentz space, and showed that the space of the multipliers from L <inf>w</inf>1(G) to A is algebrically isomorphic and homeomorphic to Ā.