The Daugavet Property of C*-Algebras and Non-commutative Lp-Spaces

The Daugavet Property of C*-Algebras and Non-commutative Lp-Spaces We prove that a C *-algebra A or a predual N * of a von Neumann algebra N has the Daugavet property if and only if A (or N) is non-atomic. We also prove a similar (although somewhat weaker) result for non-commutative L p-spaces corresponding to non-atomic von Neumann algebras. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

The Daugavet Property of C*-Algebras and Non-commutative Lp-Spaces

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2002 by Kluwer Academic Publishers
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1023/A:1012023526639
Publisher site
See Article on Publisher Site

Abstract

We prove that a C *-algebra A or a predual N * of a von Neumann algebra N has the Daugavet property if and only if A (or N) is non-atomic. We also prove a similar (although somewhat weaker) result for non-commutative L p-spaces corresponding to non-atomic von Neumann algebras.

Journal

PositivitySpringer Journals

Published: Oct 12, 2004

References

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