(APD)-property of -algebras by extensions of -algebras with (APD)

Author:
Yifeng Xue

Journal:
Proc. Amer. Math. Soc. **135** (2007), 705-711

MSC (2000):
Primary 46L05, 46L85, 46L80

Published electronically:
October 2, 2006

MathSciNet review:
2262866

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Abstract | References | Similar Articles | Additional Information

Abstract: A unital -algebra is said to have the (APD)-property if every nonzero element in has the approximate polar decomposition. Let be a closed ideal of . Suppose that and have (APD). In this paper, we give a necessary and sufficient condition that makes have (APD). Furthermore, we show that if and or is a simple purely infinite -algebra, then has (APD).

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Additional Information

**Yifeng Xue**

Affiliation:
Department of Mathematics, East China Normal University, Shanghai 200062, People’s Republic of China

Email:
yxue3486@hotmail.com

DOI:
http://dx.doi.org/10.1090/S0002-9939-06-08439-5

Keywords:
Approximate polar decomposition,
generalized inverse,
(WS)--property

Received by editor(s):
February 15, 2005

Received by editor(s) in revised form:
July 15, 2005

Published electronically:
October 2, 2006

Additional Notes:
This research was supported by the Natural Science Foundation of China and the Foundation of CSC

Communicated by:
David R. Larson

Article copyright:
© Copyright 2006
American Mathematical Society