Davood Alimohammadi
Department of Mathematics, Faculty of Science, Arak university, Arak 38156-8-8349, Iran
[ 1 ] - Nonexpansive mappings on complex C*-algebras and their fixed points
A normed space $mathfrak{X}$ is said to have the fixed point property, if for each nonexpansive mapping $T : E longrightarrow E $ on a nonempty bounded closed convex subset $ E $ of $ mathfrak{X} $ has a fixed point. In this paper, we first show that if $ X $ is a locally compact Hausdorff space then the following are equivalent: (i) $X$ is infinite set, (ii) $C_0(X)$ is infinite dimensional, (...
[ 2 ] - Quasicompact and Riesz unital endomorphisms of real Lipschitz algebras of complex-valued functions
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 pr...
[ 3 ] - Surjective Real-Linear Uniform Isometries Between Complex Function Algebras
In this paper, we first give a description of a surjective unit-preserving real-linear uniform isometry $ T : A longrightarrow B$, where $ A $ and $ B $ are complex function spaces on compact Hausdorff spaces $ X $ and $ Y $, respectively, whenever ${rm ER}left (A, Xright ) = {rm Ch}left (A, Xright )$ and ${rm ER}left (B, Yright ) = {rm Ch}left (B, Yright )$. Next, we give a description of $ T...
[ 4 ] - $(-1)$-Weak Amenability of Second Dual of Real Banach Algebras
Let $ (A,| cdot |) $ be a real Banach algebra, a complex algebra $ A_mathbb{C} $ be a complexification of $ A $ and $ | | cdot | | $ be an algebra norm on $ A_mathbb{C} $ satisfying a simple condition together with the norm $ | cdot | $ on $ A$. In this paper we first show that $ A^* $ is a real Banach $ A^{**}$-module if and only if $ (A_mathbb{C})^* $ is a complex Banach $ (A_mathbb{C})^{...
[ 5 ] - Weighted Composition Operators Between Extended Lipschitz Algebras on Compact Metric Spaces
In this paper, we provide a complete description of weighted composition operators between extended Lipschitz algebras on compact metric spaces. We give necessary and sufficient conditions for the injectivity and the sujectivity of these operators. We also obtain some sufficient conditions and some necessary conditions for a weighted composition operator between these spaces to be compact.
Co-Authors