Author： Kiselev A. V. Naboko S. N.
Publisher： Springer Publishing Company
ISSN： 0016-2663
Source： Functional Analysis and Its Applications, Vol.38, Iss.3, 2004-07, pp. : 192-201
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Abstract
We consider nonself-adjoint nondissipative trace class additive perturbations 
of a bounded self-adjoint operator 
in a Hilbert space 
. The main goal is to study the properties of the singular spectral subspace 
of 
corresponding to part of the real singular spectrum and playing a special role in spectral theory of nonself-adjoint nondissipative operators.To some extent, the properties of resemble those of the singular spectral subspace of a self-adjoint operator. Namely, we prove that and the adjoint operator 
are weakly annihilated by some scalar bounded outer analytic functions if and only if both of them satisfy the condition 
. This is a generalization of the well-known Cayley identity to nonself-adjoint operators of the above-mentioned class.
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