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Applications of amenable semigroups in operator theory

Volume 252 / 2020

Piotr Niemiec, Paweł Wójcik Studia Mathematica 252 (2020), 27-48 MSC: Primary 47D03; Secondary 43A07, 47B40, 47A15, 47H10, 46B28. DOI: 10.4064/sm180408-26-2 Published online: 18 November 2019

Abstract

The paper deals with continuous representations $\mathscr{S} \ni s \mapsto T_s \in \mathscr{L} (E)$ 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.

Authors

  • Piotr NiemiecInstytut Matematyki
    Wydział Matematyki i Informatyki
    Uniwersytet Jagielloński
    ul. Łojasiewicza 6
    30-348 Kraków, Poland
    e-mail
  • Paweł WójcikInstytut Matematyki
    Uniwersytet Pedagogiczny
    ul. Podchorążych 2
    30-084 Kraków, Poland
    e-mail

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