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Zbl 0791.47005
Brasche, Johannes; Neidhardt, Hagen; Weidmann, Joachim
On the point spectrum of selfadjoint extensions. (English)
[J] Math. Z. 214, No.2, 343-355 (1993). ISSN 0025-5874; ISSN 1432-1823/e

Let $H$ be a symmetric operator with spectral gap and infinite deficiency indices. The question is examined, to which extend the point spectrum of a selfadjoint extension $\widehat {H}$ of $H$ within the set of regular points of $H$ can be prescribed. Among others it is shown that within a spectral gap of $H$ each kind of pure point can be generated by a selfadjoint extension of $H$. The question whether von Neumann's theorem on the existence of selfadjoint extensions of $C$-real symmetric operators has a converse is answered (positively for deficiency (1,1), negatively for deficiency $(n,n)$ with $n>1$).
[J.Brasche (Frankfurt/M.)]

MSC 2000:: *47A20 Extensions and related concepts of linear operators
47B25 Symmetric and selfadjoint operators (unbounded)
47A10 Spectrum and resolvent of linear operators

Keywords: symmetric operator with spectral gap and infinite deficiency indices; point spectrum of a selfadjoint extension

Cited in: Zbl 1083.47020

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