SPECTRAL PROPERTIES OF COMMUTANTS OF UNBOUNDED SELF-ADJOINT OPERATORS WITH SIMPLE SPECTRA

ABSTRACT

An operator BImage removed. is a commutant of the unbounded Self-adjoint operator with simple spectra FImage removed. if BF⊆FB.Image removed. The properties of the commutant are determined by those of the operator FImage removed.. In this article, we show that the spectrum of these commutants is a subset of the real number set. We also establish the effect of the spectral properties of the unbounded Self-adjoint operators with simple spectra to the spectrum of its commutant. Finally, we show that the spectral measure of the unbounded Self-adjoint operator with simple spectra is a scalar multiple of that of its commutant.

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Author
Fidelis Musena Mukudi, Prof. Justus Kitheka Mile, Dr. Lucy Chikamai, Prof. Shem Omukunda Aywa.