Invariant subspaces for banach space operators with a multiply connected spectrum

Yavuz O.

INTEGRAL EQUATIONS AND OPERATOR THEORY, vol.58, no.3, pp.433-446, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 58 Issue: 3
  • Publication Date: 2007
  • Doi Number: 10.1007/s00020-007-1496-y
  • Journal Name: INTEGRAL EQUATIONS AND OPERATOR THEORY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.433-446
  • Middle East Technical University Affiliated: No

Abstract

We consider a multiply connected domain Omega = D \U (n)(j= 1) (B) over bar(lambda(j), r(j)) where D denotes the unit disk and (B) over bar(lambda(j), r(j)) subset of D denotes the closed disk centered at lambda(j) epsilon D with radius r(j) for j = 1,..., n. We show that if T is a bounded linear operator on a Banach space X whose spectrum contains delta Omega and does not contain the points lambda(1),lambda(2),...,lambda(n), and the operators T and r(j)( T -lambda I-j)(-1) are polynomially bounded, then there exists a nontrivial common invariant subspace for T* and ( T -lambda I-j)(*-1).