A NEW PROOF OF MACK'S CHARACTERIZATION OF PCS-ALGEBRAS

Title & Authors
A NEW PROOF OF MACK'S CHARACTERIZATION OF PCS-ALGEBRAS
Kim, Hyoung-Soon; Woo, Seong-Choul;

Abstract
Let A be a $\small{C^*}$-algebra and $\small{K_{A}}$ its Pedersen's ideal. A is called a PCS-algebra if the multiplier $\small{\Gamma(K_{A})\;of\;K_{A}}$ is the multiplier M(A) of A. J. Mack [5]characterized PCS-algebras by weak compactness on the spectrum of A. We give a new simple proof of this Mack's result using the concept of semicontinuity and N. C. Phillips' description of $\small{\Gamma(K_{A})}$.
Keywords
PCS-algebra;multiplier;weakly compact set;
Language
English
Cited by
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