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

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

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