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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04335-4
PII: S 0002-9939(98)04335-4
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