1Department of Mathematics Purdue University West Lafayette, IN 47907, U.S.A. 2Department of Applied Mathematics National Sun Yat-sen University Kaohsiung, 80424, Taiwan, R.O.C.
Studia Mathematica, Tome 218 (2013) no. 3, pp. 189-217
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: $\pi _p(a)(b+L)=ab+L$. A complete characterization of bounded endomorphisms of the $A$-module $A/L$ is given. The double commutant $\pi _p(A)''$ of $\pi _p(A)$ 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.
Keywords:
norm closed ideal * algebra quotient a module paper shall implement tomitas idea about representing elements multiplications complete characterization bounded endomorphisms a module given double commutant described density theorems von neumann kaplansky type obtained finally comprehensive study relative multipliers carried out
Affiliations des auteurs :
Lawrence G. Brown
1
;
Ngai-Ching Wong
2
1
Department of Mathematics Purdue University West Lafayette, IN 47907, U.S.A.
2
Department of Applied Mathematics National Sun Yat-sen University Kaohsiung, 80424, Taiwan, R.O.C.
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Lawrence G. Brown; Ngai-Ching Wong. Left quotients of a $C^*$-algebra, III: Operators on left quotients. Studia Mathematica, Tome 218 (2013) no. 3, pp. 189-217. doi: 10.4064/sm218-3-1
