


Paper's Title:
Weakly Compact Composition Operators on Real Lipschitz Spaces of Complexvalued Functions on Compact Metric Spaces with Lipschitz Involutions
Author(s):
D. Alimohammadi and H. Alihoseini
Department of Mathematics,
Faculty of Science,
Arak University
P. O. Box,3815688349,
Arak,
Iran.
Email: dalimohammadi@araku.ac.ir
Email:
hr_alihoseini@yahoo.com
URL: http://www.araku.ac.ir
Abstract:
We first show that a bounded linear operator T on a real Banach space E is weakly compact if and only if the complex linear operator T on the complex Banach space E_{C} is weakly compact, where E_{C} is a suitable complexification of E and iT' is the complex linear operator on E_{C} associated with T. Next we show that every weakly compact composition operator on real Lipschitz spaces of complexvalued functions on compact metric spaces with Lipschitz involutions is compact.
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