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Proceedings of the American Mathematical Society

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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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  • [1] P. R. Halmos, Ten problems in Hilbert space, Bull. Amer. Math. Soc. 76 (1970), 887-933. MR 42 #5066. MR 0270173 (42:5066)
  • [2] W. A. J. Luxemburg and R. F. Taylor, Almost commuting matrices are near commuting matrices, Nederl. Akad. Wetensch. Proc. Ser. A 73=Indag. Math. 32 (1970), 96-98. MR 41 #3502. MR 0258857 (41:3502)

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Keywords: Normal, subnormal operators, spectral projections, normal approximation
Article copyright: © Copyright 1974 American Mathematical Society

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