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2001 ON C¤-ALGEBRAS CUT DOWN BY CLOSED PROJECTIONS: CHARACTERIZING ELEMENTS VIA THE EXTREME BOUNDARY
Lawrence G. Brown, Ngai-Ching Wong
Taiwanese J. Math. 5(2): 433-441 (2001). DOI: 10.11650/twjm/1500407348

Abstract

Let A be a C¤ -algebra. Let z be the maximal atomic projection and p a closed projection in A¤ ¤ . It is known that x in A¤¤ has a continuous atomic part, i.e., zx = za for some a in A, whenever x is uniformly continuous on the set of pure states of A. Under some additional conditions, we shall show that if x is uniformly continuous on the set of pure states of A supported by p, or its weak* closure, then pxp has a continuous atomic part, i.e., zpxp = zpap for some a in A.

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Lawrence G. Brown. Ngai-Ching Wong. "ON C¤-ALGEBRAS CUT DOWN BY CLOSED PROJECTIONS: CHARACTERIZING ELEMENTS VIA THE EXTREME BOUNDARY." Taiwanese J. Math. 5 (2) 433 - 441, 2001. https://doi.org/10.11650/twjm/1500407348

Information

Published: 2001
First available in Project Euclid: 18 July 2017

zbMATH: 0991.46040
MathSciNet: MR1832179
Digital Object Identifier: 10.11650/twjm/1500407348

Rights: Copyright © 2001 The Mathematical Society of the Republic of China

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