Journal of Mathematical Sciences

, Volume 78, Issue 2, pp 181–194 | Cite as

Almost isometric operators: Functional model, invariant subspaces, commutant

  • V. V. Kapustin
Article
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Abstract

A new function model for an arbitrary bounded operator on a Hilbert space is constructed. This model generalizes the model of Sz.-Nagy and Foiaş for contractions and seems to be useful for operators close to an isometry (in a sense). All the model spaces are Hilbert spaces, but instead of dilation a generalization of it is used. The model admits a symmetry with respect to the map z→1/z of the complex plane. In terms of the model the question of lifting the commutant is investigated, a relationship between invariant subspaces of a unitary operator is established, and the characteristic function of the model operator is calculated. Some other problems are solved as well. Bibliography: 8 titles.

Keywords

Hilbert Space Unitary Operator Invariant Subspace Functional Model Invertible Operator 

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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • V. V. Kapustin

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