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International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 1, Pages 69-76
http://dx.doi.org/10.1155/S0161171291000066

Certain invariant subspaces for operators with rich eigenvalues

Department of Mathematics, Shiraz University, Shiraz, Iran

Received 29 September 1987; Revised 7 June 1988

Copyright © 1991 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

For a connected open subset Ω of the plane and n a positive integer, let Bn(Ω) be the space introduced by Cowen and Douglas. In this article we study the spectrum of restrictions of T in order to obtain more information about the invariant subspaces of T. When n=1 and T ϵ B1(Ω) such that σ(T)=Ω¯ is a spectral set for T we use the functional calculus we have developed for such operators to give some infinite dimensional cyclic invariant subspaces for T.