Applications of amenable semigroups in operator theory

Abstract

The paper deals with continuous homomorphisms $S\ni s\mapsto T_s\in L(E)$ of amenable semigroups $S$ into the algebra $L(E)$ of all bounded linear operators on a Banach space $E$. For a closed linear subspace $F$ of $E$, sufficient conditions are given under which there exists a projection $P\in L(E)$ onto $F$ that commutes with all $T_s$. And when $E$ is a Hilbert space, sufficient conditions are given for the existence of an invertible operator $R\in L(E)$ such that all $R{T}_s{R}^{-1}$ are isometries. Also certain results on extending intertwining operators, renorming as well as on operators on hereditarily indecomposable Banach spaces are offered.

16 pages

References in corpus (1)

• Amenable crossed product Banach algebras associated with a class of ${\mathrm{C}}^{\ast }$-dynamical systems