Abstract
We study finite dimensional perturbations of shift operators and their membership to the classes A m, n appearing in the theory of dual algebras. The results obtained yield informations about the lattice of invariant subspaces via the techniques of Scott Brown.
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References
C. APOSTOL,Ultraweakly closed operators algebras, J. Operator Theory2 (1979), 49–61.
J.A. BALL and A.LUBIN,On a class of contractive perturbations of restricted shifts, Pacific J. Math63 (1976), 309–324.
C. BENHIDA,Espaces duaux et propriétés (A m, n ), Acta Sci. Math. (Szeged)58 (1993), 431–441.
H. BERCOVICI, C. FOIAS, C. PEARCY,Dual algebras with applications to invariant subspaces and dilation theory, CBMS Regional Conf. Ser. in Math., Vol.56, Amer. Math. Soc., Providence, RI, 1985.
S. BROWN, B. CHEVREAU,Toute contraction à calcul fonctionnel isométrique est réflexive, C.R. Acad. Sci. Paris série I Math.307 (1988), 185–188.
B. CHEVREAU, G. EXNER, C. PEARCY,On the structure of contraction operators III, Michigan Math. J.36 (1989), 29–62.
D.N. CLARK,One dimensional perturbation of restricted shifts, J. Analyse Math.25 (1972), 169–191.
G.R. EXNER, Y.S. JO, I.B. JUNG,C 0 contractions: Dual operator algebras, Jordan models and multiplicity, J.O.T., to appear.
C. FOIAS and A. E. FRAZHO,The Commutant Lifting Approach To Interpolation Problems, Birkhäuser, Basel, 1990.
P.A. FUHRMANN,On a class of finite dimensional contractive perturbations of restricted shifts of finite multiplicity, Israel J. Math16 (1973), 162–176.
Y. NAKAMURA,One-dimensional perturbations of isometries, Integr. Equat. Oper. Th.9 (1986), 286–294.
Y. NAKAMURA,One-dimensional perturbations of the shift, Integr. Equat. Oper. Th.17 (1993), 373–403.
D. SARASON,Nearly invariant subspaces of the backward shift, inContributions to operator theory and its applications, Operator theory: Advances Appl., Vol.35, Birkhäuser, Basel, 1988, 481–493.
YUL. SHMULYAN,Generalized linear fractional transformations of operator balls, Sibirskii Mat. Zh.21, No. 5 (1980), 114–131. [Russian]
C.L. SIEGEL,Symplectic geometry, Amer. J. Math.65 (1943), 1–86.
B. SZ.-NAGY and C. FOIAS,Harmonic Analysis of operators on Hilbert space, North-Holland, Amsterdam, 1970.
D. TIMOTIN,Redheffer products and characteristic functions, J. Math. Anal. Appl.196 (1995), 823–840.
I. VALUŞESCU,The maximal function of a contraction, Acta Sci. Math.42 (1980), 183–188.
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Benhida, C., Timotin, D. Functional models and finite dimensional perturbations of the shift. Integr equ oper theory 29, 187–196 (1997). https://doi.org/10.1007/BF01191428
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DOI: https://doi.org/10.1007/BF01191428