Compact and quasicompact homomorphisms between differentiable Lipschitz algebras

Compact Homomorphisms of (t-algebras

Suppose A is a C*-algebra and B is a Banach algebra such that it can be continuously imbedded in B(H), the Banach algebra of bounded linear operators on some Hubert space H. It is shown that if 6 is a compact algebra homomorphism from A into B, then 6 is a finite rank operator, and the range of 0 is spanned by a finite number of idempotents. If, moreover, B is commutative, then 9 has the form 8...

Automatic Continuity of Homomorphisms Between Banach algebras and Frechet algebras

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...

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.

Certain subalgebras of Lipschitz algebras of infinitely differentiable functions and their maximal ideal spaces

We study an interesting class of Banach function algebras of innitely dierentiable functions onperfect, compact plane sets. These algebras were introduced by Honary and Mahyar in 1999, calledLipschitz algebras of innitely dierentiable functions and denoted by Lip(X;M; ), where X is aperfect, compact plane set, M = fMng1n=0 is a sequence of positive numbers such that M0 = 1 and(m+n)!Mm+n ( m!Mm)...