Amalgam Uzaylarındaki Bazı Çarpanlar ve Rölatif Tamlanış Üzerine

G, $\mu $ Haar ölçümüne sahip yerel tıkız değişmeli bir grup olsun. Bu çalışmada ilk olarak, $\left( L^{p},\ell ^{q}\right) (G)$ amalgam uzayı tanıtıldı ve bazı temel özellikleri verildi. Ayrıca $\left( L^{p},\ell ^{q}\right) (G)$ amalgam uzayının doğrusal bir A alt uzayı için bir $\overset{\sim }{A}$ rölatif tamlanış tanımlandı ve bu tamlanışın bazı özellikleri ele alındı. Son olarak; $Hom_{L^{1}(G)}\left( L^{1}(G),A\right) $ ile $\overset{\sim }{A}$ arasında cebirsel bir izomorfizma ve homeomorfizma olduğu ispatlandı.

Anahtar Kelimeler:

Amalgam uzayı, Banach modül, Rölatif tamlanış, İzomorfizma

On Some Multipliers and the Relative Completion in Amalgam Spaces

Let G be a locally compact abelian group with Haar measure $\mu $. First of all, in this paper, the amalgam space $\left( L^{p},\ell ^{q}\right) (G)$ is introduced and some basic properties of amalgam space are given. Moreover, a relative completion $\overset{\sim }{A}$ for a linear subspace A of amalgam space $\left( L^{p},\ell ^{q}\right) (G)$ is defined, and is considered several properties of it. Finally, it is proved that there is an algebraic isomorphism and homeomorphism between $Hom_{L^{1}(G)}\left( L^{1}(G),A\right) $ and $\overset{\sim }{A}$ .

Keywords:

Amalgam space, Banach module, Relative completion, Isomorphism,

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