1968/01/01 by Bruce Alan Barnes, Bruce A. Barnes
Mathematics · Computer Science · #Advanced Topics in Algebra #Matrix Theory and Algorithms #Algebraic structures and combinatorial models
paper · pdf · doi:10.4153/cjm-1968-048-2
Given an algebra A , the elements of A induce linear operators on A by left and right multiplication. Various authors have studied Banach algebras A with the property that some or all of these multiplication maps are completely continuous operators on A ; see ( 1 - 5 ). In ( 3 )1. Kaplansky defined an element u of a Banach algebra A to be completely continuous if the maps a ⟶ ua and a ⟶ au, a ∊ A , are completely continuous linear operators.