Tanja Eisner, Tamas Matrai
Published 2010-08-19, updated 2011-10-28Version 3
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.
Comments: 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
Journal: Israel J. Math. 195 (2013), 247-281
Proper splittings of Hilbert space operators
On the adjoint of Hilbert space operators
Nayak's theorem for compact operators
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