Applications of amenable semigroups in operator theory
Tom 252 / 2020
Streszczenie
The paper deals with continuous representations of amenable semigroups \mathscr{S} into the algebra \mathscr{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 \mathscr{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 L \in \mathscr{L} (E) such that all L T_s L^{-1} are isometries. Also some results on extending intertwining operators, on renorming and on operators on hereditarily indecomposable Banach spaces are offered.