Left quotients of a C*-algebra, III: Operators on left quotients

Lawrence G. Brown, Ngai-Ching Wong
2013 Studia Mathematica  
Let L be a norm closed left ideal of a C*-algebra A. Then the left quotient A/L is a left A-module. In this paper, we shall implement Tomita's idea about representing elements of A as left multiplications: πp(a)(b + L) = ab + L. A complete characterization of bounded endomorphisms of the A-module A/L is given. The double commutant πp(A) of πp(A) in B(A/L) is described. Density theorems of von Neumann and Kaplansky type are obtained. Finally, a comprehensive study of relative multipliers of A is carried out.
doi:10.4064/sm218-3-1 fatcat:q3x2smecbzd7bphpajwy673m4a