Subnormal weighted shifts and asymptotic properties of normal operators
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- by J. J. Bastian and K. J. Harrison PDF
- Proc. Amer. Math. Soc. 42 (1974), 475-479 Request permission
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.References
- P. R. Halmos, Ten problems in Hilbert space, Bull. Amer. Math. Soc. 76 (1970), 887–933. MR 270173, DOI 10.1090/S0002-9904-1970-12502-2
- 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 0258857
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 42 (1974), 475-479
- MSC: Primary 47B20
- DOI: https://doi.org/10.1090/S0002-9939-1974-0380491-X
- MathSciNet review: 0380491