Invariant subspaces for Banach space operators with an annular spectral set

Yavuz O.

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.360, no.5, pp.2661-2680, 2008 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 360 Issue: 5
  • Publication Date: 2008
  • Journal Name: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2661-2680
  • Middle East Technical University Affiliated: No

Abstract

Consider an annulus Omega = {z epsilon C : r(0) < |z| < 1} for some 0 < r(0) < 1, and let T be a bounded invertible linear operator on a Banach space X whose spectrum contains partial derivative Omega. Assume there exists a constant K > 0 such that parallel to p(T)parallel to <= K sup{vertical bar p(lambda)vertical bar : vertical bar lambda vertical bar <= 1} and parallel to p(r(0)T(-1))parallel to <= K sup{vertical bar p(lambda)vertical bar : vertical bar lambda vertical bar <= 1} for all polynomials p. Then there exists a nontrivial common invariant subspace for T* and T*(-1).