Operators on the left quotient of a C*-algebra
by
Ngai-Ching Wong
Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiun 80424, Taiwan, ROC.
Coauthors: Lawrence G. Brown (Purdue University)

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 into B(A/L) as left multiplications: \p(a)(b+L)=ab+L. A complete characterization of A-module maps in B(A/L) is given. The double commutant \p(A)'' of \p(A) in B(A/L) is described. Density theorems of von Neumann and Kaplansky type are obtained. Finally, a comprehensive study in relative multipliers of A is carried out.

http://www.math.nsysu.edu.tw/u/wong/mypub.html

Date received: June 2, 2000