Compact perturbations of isometries

Serban, Ioana; Turcu, Flavius

doi:10.1090/S0002-9939-06-08586-8

Compact perturbations of isometries
HTML articles powered by AMS MathViewer

by Ioana Serban and Flavius Turcu PDF

Proc. Amer. Math. Soc. 135 (2007), 1175-1180 Request permission

Abstract:

We give some characterizations of isometries (contractions) which are perturbations with compact operators of a given arbitrary isometry, in terms of certain natural factorizations. As a consequence we obtain general parametric representations of these perturbations.

References

Chafiq Benhida and Dan Timotin, Functional models and finite-dimensional perturbations of the shift, Integral Equations Operator Theory 29 (1997), no. 2, 187–196. MR 1472098, DOI 10.1007/BF01191428
Chafiq Benhida and Dan Timotin, Finite rank perturbations of contractions, Integral Equations Operator Theory 36 (2000), no. 3, 253–268. MR 1753419, DOI 10.1007/BF01213924
Douglas N. Clark, One dimensional perturbations of restricted shifts, J. Analyse Math. 25 (1972), 169–191. MR 301534, DOI 10.1007/BF02790036
Gilles Cassier and Dan Timotin, Power boundedness and similarity to contractions for some perturbations of isometries, J. Math. Anal. Appl. 293 (2004), no. 1, 160–180. MR 2052538, DOI 10.1016/j.jmaa.2003.12.020
Yoshihiro Nakamura, One-dimensional perturbations of isometries, Integral Equations Operator Theory 9 (1986), no. 2, 286–294. MR 837520, DOI 10.1007/BF01195012
Yoshihiro Nakamura, One-dimensional perturbations of the shift, Integral Equations Operator Theory 17 (1993), no. 3, 373–403. MR 1237960, DOI 10.1007/BF01200292