A Characterization of Jacobson Radical in Γ-Banach Algebras

Nilakshi Goswami

Department of Mathematics, Gauhati University, Guwahati, India.

DOI: 10.4236/apm.2012.26062                

Abstract

Let V₁ and V₂ be two -Banach algebras and R_i be the right operator Banach algebra and L_i be the left operator Banach algebra of V_i(i=1,2). We give a characterization of the Jacobson radical for the projective tensor product V_1rV₂ in terms of the Jacobson radical for R_1rL₂. If V₁ and V₂ are isomorphic, then we show that this characterization can also be given in terms of the Jacobson radical for R_2rL₁.

Keywords

Γ-Algebra; Right Quasi Regularity; Tensor Product; Operator Banach Algebra

Conflicts of Interest

The authors declare no conflicts of interest.

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