On Fuglede’s theorem and operator topologies

Rogers, Donald D.

doi:10.1090/S0002-9939-1979-0529207-9

On Fuglede's theorem and operator topologies

Author: Donald D. Rogers
Journal: Proc. Amer. Math. Soc. 75 (1979), 32-36
MSC: Primary 47B15
DOI: https://doi.org/10.1090/S0002-9939-1979-0529207-9
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 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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