@article {
author = {Mayghani, Maliheh and Alimohammadi, Davood},
title = {Quasicompact and Riesz unital endomorphisms of real Lipschitz algebras of complex-valued functions},
journal = {Sahand Communications in Mathematical Analysis},
volume = {09},
number = {1},
pages = {1-14},
year = {2018},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2018.24240},
abstract = {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.},
keywords = {Complexification,Lipschitz algebra,Lipschitz involution,Quasicompact operator,Riesz operator,Unital endomorphism},
url = {http://scma.maragheh.ac.ir/article_24240.html},
eprint = {http://scma.maragheh.ac.ir/article_24240_91e55951d6b21d67e1abf159e8c6f90f.pdf}
}