Smooth rank one perturbations of selfadjoint operators

Authors:
S. Hassi, H. S. V. de Snoo and A. D. I. Willemsma

Journal:
Proc. Amer. Math. Soc. **126** (1998), 2663-2675

MSC (1991):
Primary 47A55, 47A57, 47B25; Secondary 81Q15

DOI:
https://doi.org/10.1090/S0002-9939-98-04335-4

MathSciNet review:
1451805

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Abstract | References | Similar Articles | Additional Information

Abstract: Let $A$ be a selfadjoint operator in a Hilbert space $\mathfrak {H}$ with inner product $[\cdot ,\cdot ]$. The rank one perturbations of $A$ have the form $A+\tau [\cdot ,\omega ] \omega$, $\tau \in \mathbb {R}$, for some element $\omega \in \mathfrak {H}$. In this paper we consider smooth perturbations, i.e. we consider $\omega \in \operatorname {dom} |A|^{k/2}$ for some $k \in \mathbb {N} \cup \{0\}$. Function-theoretic properties of their so-called $Q$-functions and operator-theoretic consequences will be studied.

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Additional Information

**S. Hassi**

Affiliation:
Department of Statistics University of Helsinki PL 54, 00014 Helsinki Finland

Email:
hassi@cc.helsinki.fi

**H. S. V. de Snoo**

Affiliation:
Department of Mathematics University of Groningen Postbus 800, 9700 AV Groningen Nederland

Email:
desnoo@math.rug.nl

Keywords:
Rank one perturbation,
moments,
selfadjoint extension,
$Q$-function,
Friedrichs extension

Received by editor(s):
December 26, 1996

Received by editor(s) in revised form:
January 28, 1997

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1998
American Mathematical Society