Suprema of chains of operators

Suprema of chains of operators Let $${{\mathcal E}}$$ be a real Banach space of operators ordered by a cone $${{\mathcal K}}$$ . We give a sufficient condition for that each chain which is bounded above has a supremum. This condition is satisfied in several classical cases, as for the Loewner ordering on the space of all symmetric operators on a Hilbert space, for example. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Suprema of chains of operators

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Publisher
Springer Journals
Copyright
Copyright © 2010 by Springer Basel AG
Subject
Mathematics; Operator Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics; Potential Theory; Fourier Analysis
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-010-0079-3
Publisher site
See Article on Publisher Site

Abstract

Let $${{\mathcal E}}$$ be a real Banach space of operators ordered by a cone $${{\mathcal K}}$$ . We give a sufficient condition for that each chain which is bounded above has a supremum. This condition is satisfied in several classical cases, as for the Loewner ordering on the space of all symmetric operators on a Hilbert space, for example.

Journal

PositivitySpringer Journals

Published: Jul 27, 2010

References

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