1008.3326Aug 19, 201034 pages, the referee's suggestions incorporated, proof added that contractions on a separable Hilbert space form a Polish space for the weak polynomial topology. To appear in Israel J. Math

On typical properties of Hilbert space operators

Tanja Eisner, Tamas Matrai

Functional Analysis General Topology

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Abstract

We study the typical behavior of bounded linear operators on infinite dimensional complex separable Hilbert spaces in the norm, strong-star, strong, weak polynomial and weak topologies. In particular, we investigate typical spectral properties, the problem of unitary equivalence of typical operators, and their embeddability into C_0-semigroups. Our results provide information on the applicability of Baire category methods in the theory of Hilbert space operators.

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