Linear operators on the space of bounded continuous functions with strict topologies

Linear operators on the space of bounded continuous functions with strict topologies Let X be a completely regular Hausdorff space, and let C b (X) denote the Banach space of all real-valued bounded continuous functions on X. We study linear operators from C b (X) provided with the strict topology β σ to a Banach space $${(E,\|\cdot\|_E)}$$ . In particular, we derive a Yosida–Hewitt type decomposition for weakly compact operators from C b (X) to E. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Linear operators on the space of bounded continuous functions with strict topologies

Positivity , Volume 14 (4) – Jun 23, 2010
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Publisher
SP Birkhäuser Verlag Basel
Copyright
Copyright © 2010 by The Author(s)
Subject
Mathematics; Econometrics; Calculus of Variations and Optimal Control; Optimization; Potential Theory; Operator Theory; Fourier Analysis
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-010-0068-6
Publisher site
See Article on Publisher Site

Abstract

Let X be a completely regular Hausdorff space, and let C b (X) denote the Banach space of all real-valued bounded continuous functions on X. We study linear operators from C b (X) provided with the strict topology β σ to a Banach space $${(E,\|\cdot\|_E)}$$ . In particular, we derive a Yosida–Hewitt type decomposition for weakly compact operators from C b (X) to E.

Journal

PositivitySpringer Journals

Published: Jun 23, 2010

References

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