Journal of Mathematical Sciences

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

Almost isometric operators: Functional model, invariant subspaces, commutant

  • V. V. Kapustin


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.


Hilbert Space Unitary Operator Invariant Subspace Functional Model Invertible Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • V. V. Kapustin

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