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

Lawrence G. Brown, and Ngai-Ching Wong. "Left quotients of a C*-algebra, III: Operators on left quotients." Studia Mathematica 218.3 (2013): 189-217. <http://eudml.org/doc/285821>.

@article{LawrenceG2013,
abstract = {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 $π_\{p\}(A)^\{\prime \prime \}$ 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.},
author = {Lawrence G. Brown, Ngai-Ching Wong},
journal = {Studia Mathematica},
keywords = {-algebras; continuous fields of Hilbert spaces; left regular representations; multipliers; density theorems},
language = {eng},
number = {3},
pages = {189-217},
title = {Left quotients of a C*-algebra, III: Operators on left quotients},
url = {http://eudml.org/doc/285821},
volume = {218},
year = {2013},
}

TY - JOUR
AU - Lawrence G. Brown
AU - Ngai-Ching Wong
TI - Left quotients of a C*-algebra, III: Operators on left quotients
JO - Studia Mathematica
PY - 2013
VL - 218
IS - 3
SP - 189
EP - 217
AB - 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 $π_{p}(A)^{\prime \prime }$ 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.
LA - eng
KW - -algebras; continuous fields of Hilbert spaces; left regular representations; multipliers; density theorems
UR - http://eudml.org/doc/285821
ER -