The Australian Journal of Mathematical Analysis and Applications

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ISSN 1449-5910  


Paper Information

Paper Title:

Weakly Compact Composition Operators on Real Lipschitz Spaces of Complex-valued Functions on Compact Metric Spaces with Lipschitz Involutions


D. Alimohammadi and H. Alihoseini

Department of Mathematics,
Faculty of Science, Arak University
P. O. Box,38156-8-8349, Arak,


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 EC is weakly compact, where EC is a suitable complexification of E and iT' is the complex linear operator on EC associated with T. Next we show that every weakly compact composition operator on real Lipschitz spaces of complex-valued functions on compact metric spaces with Lipschitz involutions is compact.

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