Domination problem on Banach lattices and almost weak compactness

Domination problem on Banach lattices and almost weak compactness In this paper we give several new results concerning domination problem in the setting of positive operators between Banach lattices. Mainly, it is proved that every positive operator $$R$$ R on a Banach lattice $$E$$ E dominated by an almost weakly compact operator $$T$$ T satisfies that the $$R^2$$ R 2 is almost weakly compact. Domination by strictly singular operators is also considered. Moreover, we present some interesting connections between strictly singular, disjointly strictly singular and almost weakly compact operators. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Domination problem on Banach lattices and almost weak compactness

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Publisher
Springer Basel
Copyright
Copyright © 2015 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/s11117-015-0328-6
Publisher site
See Article on Publisher Site

Abstract

In this paper we give several new results concerning domination problem in the setting of positive operators between Banach lattices. Mainly, it is proved that every positive operator $$R$$ R on a Banach lattice $$E$$ E dominated by an almost weakly compact operator $$T$$ T satisfies that the $$R^2$$ R 2 is almost weakly compact. Domination by strictly singular operators is also considered. Moreover, we present some interesting connections between strictly singular, disjointly strictly singular and almost weakly compact operators.

Journal

PositivitySpringer Journals

Published: Feb 4, 2015

References

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