%0 Journal Article
%T Quasicompact and Riesz unital endomorphisms of real Lipschitz algebras of complex-valued functions
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Mayghani, Maliheh
%A Alimohammadi, Davood
%D 2018
%\ 01/01/2018
%V 09
%N 1
%P 1-14
%! Quasicompact and Riesz unital endomorphisms of real Lipschitz algebras of complex-valued functions
%K Complexification
%K Lipschitz algebra
%K Lipschitz involution
%K Quasicompact operator
%K Riesz operator
%K Unital endomorphism
%R 10.22130/scma.2018.24240
%X We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompactÂ (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we prove that every unital endomorphism of real Lipschitz algebras of complex-valued functions on compact metric spaces with Lipschitz involutions is a composition operator. Finally, we study some properties of quasicompact and Riesz unital endomorphisms of these algebras.
%U http://scma.maragheh.ac.ir/article_24240_91e55951d6b21d67e1abf159e8c6f90f.pdf