We prove a general operator theoretic result that asserts that many multiplicity two selfadjoint operators have simple singular spectrum. © 2005 Elsevier Inc. All rights reserved.

Let X1,…,Xn be operators in a finite von Neumann algebra and consider their division closure the affiliated unbounded operators. We address question when this is skew field (aka ring) it free field. show that first property equivalent to strong Atiyah second can characterized terms of noncommutative distribution X1,…,Xn. More precisely, generate if only there exist no non-zero rank T1,…,Tn such...

Selfadjoint Sturm-Liouville operators Hω on L2(a, b) with random potentials are considered and it is proven, using positivity conditions, that for almost every ω the operator Hω does not share eigenvalues with a broad family of random operators and in particular with operators generated in the same way as Hω but in L2(ã, b̃) where (ã, b̃) ⊂ (a, b).

We give general spectral and eigenvalue perturbation bounds for a selfadjoint operator perturbed in the sense of the pseudo-Friedrichs extension. We also give several generalisations of the aforementioned extension. The spectral bounds for finite eigenvalues are obtained by using analyticity and monotonicity properties (rather than variational principles) and they are general enough to include ...

The theory of symmetric, non-selfadjoint operators has several deep applications to the complex function theory of certain reproducing kernel Hilbert spaces of analytic functions, as well as to the study of ordinary differential operators such as Schrodinger operators in mathematical physics. Examples of simple symmetric operators include multiplication operators on various spaces of analytic f...