Operator Inequalities Implying Similarity to a Contraction

Bello-Burguet, Glenier; Yakubovich, Dmitry ✉

Angol nyelvű Tudományos Szakcikk (Folyóiratcikk)
  • SJR Scopus - Computational Theory and Mathematics: Q2
    Let T be a bounded linear operator on a Hilbert space H such thatalpha[T*,T]:=Sigma(infinity)(n=0)alpha(nTTn)-T-*n >= 0,where alpha(t)=Sigma(infinity)(n=0)alpha(n)t(n) is a suitable analytic function in the unit disc D with real coefficients. We prove that if alpha(t)=(1-t)(alpha) over tilde (t), where (alpha) over tilde has no zeros in [0,1], then T is similar to a contraction. Operators of this type have been investigated by Agler, Muller, Olofsson, Pott and others, however, we treat cases where their techniques do not apply. We write down an explicit Nagy-Foias type model of an operator in this class and discuss its usual consequences (completeness of eigenfunctions, similarity to a normal operator, etc.). We also show that the limits of parallel to T(n)h parallel to as n -> infinity, h is an element of H, do not exist in general, but do exist if an additional assumption on alpha is imposed. Our approach is based on a factorization lemma for certain weighted Wiener algebras.
    Hivatkozás stílusok: IEEEACMAPAChicagoHarvardCSLMásolásNyomtatás
    2021-10-23 10:41