Vol. 34, No. 3, 1970

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The peturbation of the singular spectrum

Richard Hindman Bouldin

Vol. 34 (1970), No. 3, 569–583

This paper designates a subset of the spectrum of a bounded self adjoint operator on a complex separable Hilbert space. The set is called the singular spectrum and is distinguished by the fact that it is a support for the singular part of the spectral measure of the operator. The behavior of the singular spectrum, when the operator is perturbed by a bounded self adjoint operator, is studied. The thrust of these results is to give conditions sufficient for the perturbed operator to have no singular spectrum.

Mathematical Subject Classification
Primary: 47.48
Received: 12 January 1970
Published: 1 September 1970
Richard Hindman Bouldin