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

• Autorzy: Giorgos Petsoulas , Theocharis Raikoftsalis
• Języki publikacji: EN

Abstrakty

EN

The famous Gowers tree space is the first example of a space not containing c₀, ℓ₁ or a reflexive subspace. We present a space with a similar construction and prove that it is hereditarily indecomposable (HI) and has ℓ₂ as a quotient space. Furthermore, we show that every bounded linear operator on it is of the form λI + W where W is a weakly compact (hence strictly singular) operator.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B26: Nonseparable Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 190
• Numer: 3
• Strony: 233-281

Daty

wydano

2009

Twórcy

autor

Giorgos Petsoulas

• Department of Mathematics, Faculty of Applied Sciences, National Technical University of Athens, Zografou Campus, 157 80, Athens, Greece

autor

Theocharis Raikoftsalis

• Department of Mathematics, Faculty of Applied Sciences, National Technical University of Athens, Zografou Campus, 157 80, Athens, Greece

Identyfikatory

DOI

10.4064/sm190-3-2