Left quotients of ac*-algebra, i: representation via vector sections

Ngai-Ching Wong

Functional Analysis mathscidoc:1910.43709

Journal of Operator Theory, 185-201, 1994.7
Let A be a C*-algebra, L a closed left ideal of A and p the closed projection related to L. We show that for an xp in A**p ( A**/L**) if pAxp pAp and px*xp pAp then xp Ap ( A/L). The proof goes by interpreting elements of A**p (resp. Ap) as admissible (resp. continuous admissible) vector sections over the base space F(p) = { A* : 0, (p) = 1} in the notions developed by Diximier and Douady, Fell, and Tomita. We consider that our results complement both Kadison function representation and Takesaki duality theorem.
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@inproceedings{ngai-ching1994left,
  title={LEFT QUOTIENTS OF AC*-ALGEBRA, I: REPRESENTATION VIA VECTOR SECTIONS},
  author={Ngai-Ching Wong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020211428858629238},
  booktitle={Journal of Operator Theory},
  pages={185-201},
  year={1994},
}
Ngai-Ching Wong. LEFT QUOTIENTS OF AC*-ALGEBRA, I: REPRESENTATION VIA VECTOR SECTIONS. 1994. In Journal of Operator Theory. pp.185-201. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020211428858629238.
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