Operators on a Hilbert space similar to a part of the backward shift of multiplicity one
Tom 147 / 2001
Studia Mathematica 147 (2001), 27-35
MSC: 47A10, 47A11.
DOI: 10.4064/sm147-1-3
Streszczenie
Let 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.
