Real operator algebras and real completely isometric theory

Real operator algebras and real completely isometric theory This paper is a continuation of the program started by Ruan (Acta Math Sin (Engl Ser) 19(3):485–496, 2003, Illinois J Math 47(4):1047–1062, 2003), of developing real operator space theory. In particular, we develop the theory of real operator algebras. We also show among other things that the injective envelope, $$C^*$$ -envelope and non-commutative Shilov boundary exist for a real operator space. We develop real one-sided $$M$$ -ideal theory and characterize one-sided $$M$$ -ideals in real $$C^*$$ -algebras and real operator algebras with contractive approximate identity. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Real operator algebras and real completely isometric theory

Positivity , Volume 18 (1) – Apr 6, 2013
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Publisher
Springer Basel
Copyright
Copyright © 2013 by Springer Basel
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.
10.1007/s11117-013-0233-9
Publisher site
See Article on Publisher Site

Abstract

This paper is a continuation of the program started by Ruan (Acta Math Sin (Engl Ser) 19(3):485–496, 2003, Illinois J Math 47(4):1047–1062, 2003), of developing real operator space theory. In particular, we develop the theory of real operator algebras. We also show among other things that the injective envelope, $$C^*$$ -envelope and non-commutative Shilov boundary exist for a real operator space. We develop real one-sided $$M$$ -ideal theory and characterize one-sided $$M$$ -ideals in real $$C^*$$ -algebras and real operator algebras with contractive approximate identity.

Journal

PositivitySpringer Journals

Published: Apr 6, 2013

References

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