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

Giorgos Petsoulas; Theocharis Raikoftsalis — 2009

Studia Mathematica

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.

The cofinal property of the reflexive indecomposable Banach spaces

Spiros A. Argyros; Theocharis Raikoftsalis — 2012

Annales de l’institut Fourier

It is shown that every separable reflexive Banach space is a quotient of a reflexive hereditarily indecomposable space, which yields that every separable reflexive Banach is isomorphic to a subspace of a reflexive indecomposable space. Furthermore, every separable reflexive Banach space is a quotient of a reflexive complementably $ℓ_{p}$ -saturated space with $1 < p < \infty$ and of a $c_{0}$ saturated space.

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