Multipliers and the relative completion in L-w(p)(G)

Abstract

Quek and Yap defined a relative completion A for a linear subspace A of L-p(G), 1 <= p < infinity; and proved that there is an isometric isomorphism, between HOML1(G),(L-1(G), A) and <(A)over tilde>, where Hom(L1(G))(L-1(G),A) is the space of the module homomorphisms (or multipliers) from L-1(G) to A. In the present, we defined a relative completion for a linear subspace (A) over tilde of L-w(p)(G) where w is a Beurling's weighted function and LP.(G) is the weighted LP(G) space, ([14]). Also, we proved that there is an algeabric isomorphism and homeomorphism, between Hom(Lw1(G))(L-w(1)(G), A) and (A) over tilde. At the end of this work we gave some applications and examples.