On typical properties of Hilbert space operators

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.

34 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

References in corpus (4)

• Category theorems for stable operators on Hilbert spaces
• A hereditarily indecomposable L_\infty-space that solves the scalar-plus-compact problem
• Rigidity of contractions on Hilbert spaces
• Typical operators admit common cyclic vectors

Cited by in corpus (1)

• Typical operators admit common cyclic vectors