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