Random sets of isomorphism of linear operators on Hilbert space
نویسنده
چکیده
Abstract: This note deals with a problem of the probabilistic Ramsey theory in functional analysis. Given a linear operator T on a Hilbert space with an orthogonal basis, we define the isomorphic structure Σ(T ) as the family of all subsets of the basis so that T restricted to their span is a nice isomorphism. Our main result is a dimension-free optimal estimate of the size of Σ(T ). It improves and extends in several ways the principle of restricted invertibility due to Bourgain and Tzafriri. With an appropriate notion of randomness, we obtain a randomized principle of restricted invertibility.
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