Multipliers and the relative completion in $\L^p_w(G)$

Abstract

Quek and Yap defined a relative completion \widetilde A for a linear subspace A of Lp(G), 1\leq p < \infty; and proved that there is an isometric isomorphism, between Hom_{L1(G)}(L1(G), A) and \widetilde A, where Hom_{L1(G)}(L1(G),A) is the space of the module homomorphisms (or multipliers) from L1(G) to A. Inth e present, we defined a relative completion \widetilde A for a linear subspace A of Lp_w(G) ,where w is a Beurling‘s weighted function and Lp_w(G) is the weighted Lp(G) space, ([14]). Also, we proved that there is an algeabric isomorphism and homeomorphism, between Hom_{L1_w(G)}(L1_w(G),A) and \widetilde A. At the end of this work we gave some applications and examples.