Abstract
We construct a separable Banach space X w h with an unconditional basis that is a weak Hilbert space and no block subspace is linearly isomorphic to any of its proper subspaces. We prove that the space X w h satisfies these properties by showing it is strongly asymptotic ℓ 2 and that every bounded linear operator on X w h is a strictly singular perturbation of a diagonal operator with respect to the unit vector basis.
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