Domination conditions and spectral multiplicity of operators

Karaev M. T.

ACTA MATHEMATICA HUNGARICA, vol.134, pp.79-98, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 134
  • Publication Date: 2012
  • Doi Number: 10.1007/s10474-011-0128-9
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.79-98
  • Süleyman Demirel University Affiliated: No


We study the spectral multiplicity for the direct sum A. B of operators A and B on the Banach spaces X and Y. Under some domination conditions parallel to P(B)parallel to <= C parallel to P(Lambda)parallel to(A),in particular,parallel to B-n parallel to <= parallel to Lambda(n)parallel to, n >= 0, we prove the addition formulas mu(A circle plus B) = mu(A) + mu(B) for spectral multiplicities. We give valuable new applications of the main result of the author's paper [12]. We also use the so-called Borel transformation and generalized Duhamel product in calculating the spectral multiplicity of a direct sum of the form T circle plus A, where T is a weighted shift operator on the Wiener algebra W(D).