The spectrum of seminormal operators.

Abstract:

:With every pair of bounded self-adjoint operators {U,V} on Hilbert space such that VU - UV = (1/pii)C, where C is trace class, there is associated a certain function of two complex variables called the determining function of the pair. It was previously shown how the determining function can be obtained as the solution of a certain Riemann-Hilbert problem canonically associated with the pair, and how the complete spectral multiplicity theory for both U and V can be obtained from the determining function. We now show, under the condition that C is semidefinite, that the determining function method leads to a simple characterization of the spectrum of the seminormal operator T = U + iV.

authors

Pincus JD

doi

10.1073/pnas.68.8.1684

keywords:

subject

Has Abstract

pub_date

1971-08-01 00:00:00

pages

1684-5

issue

8

eissn

0027-8424

issn

1091-6490

journal_volume

68

pub_type

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