On typical properties of Hilbert space operators
Functional Analysis
2014-05-01 v3 General Topology
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.
Cite
@article{arxiv.1008.3326,
title = {On typical properties of Hilbert space operators},
author = {Tanja Eisner and Tamas Matrai},
journal= {arXiv preprint arXiv:1008.3326},
year = {2014}
}
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