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A Subnormal Operator and its Dual

Published online by Cambridge University Press:  20 November 2018

Robert F. Olin  and
Liming Yang
Robert F. Olin
Affiliation:
Department of Mathematics, Virginia Tech, Blacksburg, Virgina 24061, U.S.A.
Liming Yang
Affiliation:
Department of Mathematics, Virginia Tech, Blacksburg, Virgina 24061, U.S.A.
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Abstract

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It is shown that the essential spectrum of a cyclic, self-dual, subnormal operator is symmetric with respect to the real axis. The study of the structure of a cyclic, irreducible, self-dual, subnormal operator is reduced to the operator Sμ with bpeμ = D. Necessary and sufficient conditions for a cyclic subnormal operator Sμ with bpeμ = D to be self-dual are obtained under the additional assumption that the measure on the unit circle is log-integrable. Finally, an approach to a general cyclic, self-dual, subnormal operator is discussed.

Keywords

42B2030H05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 2 , 01 April 1996 , pp. 381 - 396
Copyright
Copyright © Canadian Mathematical Society 1996

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