Paper's Title:

Weakly Compact Composition Operators on Real Lipschitz Spaces of Complex-valued 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,38156-8-8349, Arak,
Iran.
E-mail: d-alimohammadi@araku.ac.ir
E-mail: 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 complex-valued functions on compact metric spaces with Lipschitz involutions is compact.

Search and serve lasted 1 second(s).