Integral Equations and Operator Theory

, Volume 68, Issue 4, pp 473–485

A Reflexivity Result Concerning Banach Space Operators with a Multiply Connected Spectrum

Authors

    • Faculty of Engineering and Natural SciencesSabanci University
Article

DOI: 10.1007/s00020-010-1818-3

Cite this article as:
Yavuz, O. Integr. Equ. Oper. Theory (2010) 68: 473. doi:10.1007/s00020-010-1818-3
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Abstract

We consider a multiply connected domain Ω which is obtained by removing n closed disks which are centered at λj with radius rj for j = 1, . . . , n from the unit disk. We assume that T is a bounded linear operator on a separable reflexive Banach space whose spectrum contains ∂Ω and does not contain the points λ1, λ2, . . . , λn, and the operators T and rj(T − λjI)−1 are polynomially bounded. Then either T has a nontrivial hyperinvariant subspace or the WOT-closure of the algebra {f(T) : f is a rational function with poles off \({\overline\Omega}\)} is reflexive.

Mathematics Subject Classification (2010)

Primary 47A15Secondary 47A60

Keywords

Invariant subspacesreflexive operator algebraspolynomially bounded operatorsfunctional calculus
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