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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Subnormal weighted shifts and asymptotic properties of normal operators


Authors: J. J. Bastian and K. J. Harrison
Journal: Proc. Amer. Math. Soc. 42 (1974), 475-479
MSC: Primary 47B20
MathSciNet review: 0380491
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Abstract: By Fuglede's theorem, an operator which commutes with a normal operator N must also commute with all spectral projections of N. We show that only in special cases is the theorem true when ``near-commutativity'' replaces ``commutativity". We show too that the restriction of a normal operator to an almost reducing subspace may be far from all normal operators on the subspace.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0380491-X
PII: S 0002-9939(1974)0380491-X
Keywords: Normal, subnormal operators, spectral projections, normal approximation
Article copyright: © Copyright 1974 American Mathematical Society