Abstract
In this paper we find a relation between the lattice of hyperinvariant subspaces of an operatorT of classC 0 over a multiply connected region and that of its Jordan modelT′. It is shown that, generally, the lattice corresponding toT′ can be identified with a retract of that corresponding toT. Thus the Jordan model has the smallest lattice of hyperinvariant subspaces in a given quasisimilarity class.
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References
H. Bercovici,C 0-Fredholm operators II, Acta Sci. Math. (Szeged)42 (1980) 3–42
H. Bercovici,Operator theory and arithmetic in H ∞, Amer. Math. Soc., Providence, 1988.
H. Bercovici and A. Zucchi,Generalized interpolation over multiply connected regions, Proc. Amer. Math. Soc.124 (1996) 2109–2113.
S. Fisher,Function theory on planar domains, a second course in complex analysis, Wiley, New York, 1983.
V. Pata and A. Zucchi,Reflexivity of C 0-operators over a multiply connected region, J. Operator Theory, to appear.
B. Sz.-Nagy and C. Foias,Sur les contractions de l'espace de Hilbert. VII. Trianulations canoniques, fonctions minimum, Acta Sci. Math. (Szeged)25 (1964) 12–37.
W. Rudin,Analytic functions of class H p , Trans. Amer. Math. Soc.78 (1955) 46–66.
A. Zucchi, Ph.D. Dissertation, Indiana University, Bloomington (1994)
A. Zucchi,Operators of class C 0 with spectra in multiply connected regions, Mem. Amer. Math. Soc.127 n.607 (1997)
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Pata, V., Zucchi, A. Hyperinvariant subspaces ofC 0-operators over a multiply connected region. Integr equ oper theory 36, 241–250 (2000). https://doi.org/10.1007/BF01202098
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DOI: https://doi.org/10.1007/BF01202098