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On the contractibility to a point of the linear groups of reflexive non-commutative Lp-spaces

Published online by Cambridge University Press:  24 October 2008

Sergei V. Ferleger  and
Fyodor A. Sukochev
Sergei V. Ferleger
Affiliation:
Department of Mathematics, Pennsylvania State University, 218 McAllister Building, PA 16802–6401, U.S.A.
Fyodor A. Sukochev
Affiliation:
Department of Mathematics and Statistics, The Flinders University of South Australia, GPO Box 2100, Adelaide 5001, Australia
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Extract

For every Banach space X, denote by GL(X) the linear group of X, i.e. the group of all linear continuous invertible operators on X with the topology induced by the operator norm. One says that GL(X) is contractible to a point if there exists a continuous map F: GL(X) × [0, 1] → GL(X) such that F(A,0) = A and F(A, 1) = Id, for every A ∈ GL(X).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 3 , April 1996 , pp. 545 - 560
Copyright
Copyright © Cambridge Philosophical Society 1996

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