Operators on a Hilbert space similar to a part of the backward shift of multiplicity one
Volume 147 / 2001
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 $1$.
