# 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

, Volume 14 (4) – Jun 23, 2010
9 pages

/lp/springer_journal/linear-operators-on-the-space-of-bounded-continuous-functions-with-SNZv175gdA
Publisher
SP Birkhäuser Verlag Basel
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

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