English

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.

Keywords

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

R2 v1 2026-06-21T16:02:55.168Z