2009
DOI: 10.4064/sm190-3-2
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A Gowers tree like space and the space of its bounded linear operators

Abstract: Abstract. The famous Gowers tree space is the first example of a space not containing c0, 1 or a reflexive subspace. We present a space with a similar construction and prove that it is hereditarily indecomposable (HI) and has 2 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.

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“…The structure of L(X) has been also studied for non-reflexive HI spaces ( [13], [4], [27]). It is notable that in all these examples, each strictly singular operator T ∈ L(X) is a weakly compact one.…”
Section: Introductionmentioning
confidence: 99%
“…The structure of L(X) has been also studied for non-reflexive HI spaces ( [13], [4], [27]). It is notable that in all these examples, each strictly singular operator T ∈ L(X) is a weakly compact one.…”
Section: Introductionmentioning
confidence: 99%