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

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Brown L., Wong N.-C.

Studia Mathematica

2013

tom 218

nr 3

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: $π_{p}(a)(b + L) = ab + L$. 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.

Ograniczanie wyników

1 Studia Mathematica

1 Brown L.

1 Wong N.-C.

1 2013

Wyniki wyszukiwania

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