Real rank and squaring mappings for unital -algebras

Authors:
A. Chigogidze, A. Karasev and M. Rørdam

Journal:
Proc. Amer. Math. Soc. **132** (2004), 783-788

MSC (2000):
Primary 46L05; Secondary 46L85, 54F45

DOI:
https://doi.org/10.1090/S0002-9939-03-07102-8

Published electronically:
August 19, 2003

MathSciNet review:
2019956

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Abstract | References | Similar Articles | Additional Information

Abstract: It is proved that if is a compact Hausdorff space of Lebesgue dimension , then the squaring mapping , defined by , is open if and only if . Hence the Lebesgue dimension of can be detected from openness of the squaring maps . In the case it is proved that the map , from the selfadjoint elements of a unital -algebra into its positive elements, is open if and only if is isomorphic to for some compact Hausdorff space with .

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Additional Information

**A. Chigogidze**

Affiliation:
Department of Mathematics and Statistics, University of Saskatchewan, McLean Hall, 106 Wiggins Road, Saskatoon, SK, S7N 5E6, Canada

Email:
chigogid@math.usask.ca

**A. Karasev**

Affiliation:
Department of Mathematics and Statistics, University of Saskatchewan, McLean Hall, 106 Wiggins Road, Saskatoon, SK, S7N 5E6, Canada

Email:
karasev@math.usask.ca

**M. Rørdam**

Affiliation:
Department of Mathematics, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark

Email:
mikael@imada.sdu.dk

DOI:
https://doi.org/10.1090/S0002-9939-03-07102-8

Keywords:
Real rank,
bounded rank,
Lebesgue dimension

Received by editor(s):
February 15, 2002

Received by editor(s) in revised form:
October 28, 2002

Published electronically:
August 19, 2003

Additional Notes:
The first named author was partially supported by an NSERC research grant

Communicated by:
David R. Larson

Article copyright:
© Copyright 2003
American Mathematical Society