A geometrical property of causal invertible systems.
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.
Let μ be a finite positive Borel measure on [0,1). Let be the Hankel matrix with entries . The matrix induces formally an operator on the space of all analytic functions in the unit disc by the fomula , z ∈ , where is an analytic function in . We characterize those positive Borel measures on [0,1) such that for all f in the Hardy space H¹, and among them we describe those for which is bounded and compact on H¹. We also study the analogous problem for the Bergman space A².