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

• Autorzy: Yoichi Uetake
• Języki publikacji: EN

Abstrakty

EN

Let A: X → X be a bounded operator on a separable complex Hilbert space X with an inner product $⟨·,·⟩_{X}$. For b, c ∈ X, a weak resolvent of A is the complex function of the form $⟨(I-zA)^{-1}b,c⟩_{X}$. 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.

Kategorie tematyczne

• 47A11: Local spectral properties
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 147
• Numer: 1
• Strony: 27-35

Daty

wydano

2001

Twórcy

autor

Yoichi Uetake

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland

Identyfikatory

DOI

10.4064/sm147-1-3