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

• Autorzy: Lawrence G. Brown , Ngai-Ching Wong
• Języki publikacji: EN

Abstrakty

EN

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: $π_{p}(a)(b + L) = ab + L$. A complete characterization of bounded endomorphisms of the A-module A/L is given. The double commutant $π_{p}(A)''$ of $π_{p}(A)$ 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.

Kategorie tematyczne

• 46L05: General theory of C * -algebras
• 46L45: Decomposition theory for C * -algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 218
• Numer: 3
• Strony: 189-217

Daty

wydano

2013

Twórcy

autor

Lawrence G. Brown

• Department of Mathematics, Purdue University, West Lafayette, IN 47907, U.S.A.

autor

Ngai-Ching Wong

• Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 80424, Taiwan, R.O.C.

Identyfikatory

DOI

10.4064/sm218-3-1