Almost isometric operators: a function model, invariant subspaces, the~commutant
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 20, Tome 201 (1992), pp. 95-116
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A new function model for an arbitrary bounded operator on 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 simmetry relative to the map $z\mapsto1/z$ of the complex plane. In terms of the model the question of lifting of the commutant is investigated, a relationship between invariant subspaces of a unitary operator is established, the characteristic function of the model operator is calculated. Some other problems are solved as well.
@article{ZNSL_1992_201_a2,
author = {V. V. Kapustin},
title = {Almost isometric operators: a function model, invariant subspaces, the~commutant},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {95--116},
publisher = {mathdoc},
volume = {201},
year = {1992},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1992_201_a2/}
}
V. V. Kapustin. Almost isometric operators: a function model, invariant subspaces, the~commutant. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 20, Tome 201 (1992), pp. 95-116. http://geodesic.mathdoc.fr/item/ZNSL_1992_201_a2/