Operators on a Hilbert space similar to a part of the backward shift of multiplicity one

Volume 147 / 2001

Yoichi Uetake Studia Mathematica 147 (2001), 27-35 MSC: 47A10, 47A11. DOI: 10.4064/sm147-1-3

Abstract

Let $A :X \to X$ be a bounded operator on a separable complex Hilbert space $X$ with an inner product $\langle \cdot , \cdot \rangle _X$. For $b, c \in X$, a weak resolvent of $A$ is the complex function of the form $\langle (I-zA)^{-1}b, c \rangle _X$. We will discuss an equivalent condition, in terms of weak resolvents, for $A$ to be similar to a restriction of the backward shift of multiplicity $1$.

Authors

  • Yoichi UetakeFaculty of Mathematics and Computer Science
    Adam Mickiewicz University
    Matejki 48/49
    60-769 Poznań, Poland
    e-mail

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