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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On Fuglede's theorem and operator topologies


Author: Donald D. Rogers
Journal: Proc. Amer. Math. Soc. 75 (1979), 32-36
MSC: Primary 47B15
MathSciNet review: 529207
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Abstract: For each normal operator N and neighborhood E of 0 in the strong or weak operator topology there is a neighborhood D of 0 in the same topology such that $ \left\Vert B \right\Vert \leqslant 1$ and $ NB - BN$ in D imply $ {N^\ast}B - B{N^\ast}$ in E. An example is given to show that D depends on N as well as E.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0529207-9
Keywords: Normal operator, subnormal operator, Fuglede theorem, operator topology
Article copyright: © Copyright 1979 American Mathematical Society