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Davood Alimohammadi

Davood Alimohammadi

Academic rank: Associate Professor
ORCID: https://orcid.org/0000-0002-9398-6213
Education: PhD.
ScopusId: 6505995626
Faculty: Science
Address: Arak University
Phone:

Research

Title
Quasicompact and Riesz unital endomorphisms of real Lipschitz algebras of complex-valued functions
Type
JournalPaper
Keywords
Complexi cation, Lipschitz algebra, Lipschitz involution,
Year
2018
Journal Sahand Communications in Mathematical Analysis
DOI
Researchers Davood Alimohammadi ، MALIHEH MAYGHANI

Abstract

‎We first show that every unital endomorphism of real Lipschitz algebras of compl‎ ‎ex-valued functions on compact metric spaces with Lipschitz involutions is a composition operator‎. ‎Next we establish a formula for essential spectral radius of a unital endomorphism $ T $ of these algebras under a condition which is equivalent to the quasicompactness of the endomorphism $ T $‎. ‎We also conclude a necessary and sufficient condition for a unital endomorphism of these algebras to be Riesz‎. ‎Moreover‎, ‎we get a relation for the spectrum and the set of eigenvalues of quasicompact and Riesz endomorphism of these algebras‎. %Finally, ‎we show that the class of quasicompact (Riesz‎, ‎respectively) unital endomorphisms of these algebras is larger that the class of quasicompact (Riesz‎, ‎respectively) unital endomorphisms of complex Lipschitz algebras as real Banach algebras‎.d