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, 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. 2000 Mathematics Subject Classification: 46B20, 46B26.
doi:10.4064/sm190-3-2 fatcat:emdjv2eppnde5hm5gwqhpfzbta