Compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions

Subject Areas : Functional analysis

D.  Alimohammadi ¹ (Department of Mathematics, Faculty of Science, Arak University, Arak, 38156-8-8349, Iran)
S.  Sefidgar ² (Department of Mathematics, Faculty of Science, Arak University, Arak, 38156-8-8349, Iran)

Received: 2014-07-28 Accepted : 2014-09-29 Published : 2014-10-12

Keywords: Compact operator, composition operator, Lipschitz function, spectrum of an operator, Lipschitz involution,

Abstract :

We characterize compact composition operators on real Banach spaces ofcomplex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, withLipschitz involutions and determine their spectra.

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