A Gowers tree like space and the space of its bounded linear operators

Tom 190 / 2009

Giorgos Petsoulas, Theocharis Raikoftsalis Studia Mathematica 190 (2009), 233-281 MSC: 46B20, 46B26. DOI: 10.4064/sm190-3-2

Streszczenie

The famous Gowers tree space is the first example of a space not containing $c_0$, $\ell _1$ or a reflexive subspace. We present a space with a similar construction and prove that it is hereditarily indecomposable (HI) and has $\ell _2$ as a quotient space. Furthermore, we show that every bounded linear operator on it is of the form $\lambda I+W$ where $W$ is a weakly compact (hence strictly singular) operator.

Autorzy

  • Giorgos PetsoulasDepartment of Mathematics
    Faculty of Applied Sciences
    National Technical University of Athens
    Zografou Campus
    157 80, Athens, Greece
    e-mail
  • Theocharis RaikoftsalisDepartment of Mathematics
    Faculty of Applied Sciences
    National Technical University of Athens
    Zografou Campus
    157 80, Athens, Greece
    e-mail

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