PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

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


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.


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

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image