@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 quasicompact  (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 = {https://scma.maragheh.ac.ir/article_24240.html}, eprint = {https://scma.maragheh.ac.ir/article_24240_91e55951d6b21d67e1abf159e8c6f90f.pdf} }