On Fuglede’s theorem and operator topologies
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- by Donald D. Rogers PDF
- Proc. Amer. Math. Soc. 75 (1979), 32-36 Request permission
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 $\left \| B \right \| \leqslant 1$ 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.References
- Errett Bishop, Spectral theory for operators on a Banach space, Trans. Amer. Math. Soc. 86 (1957), 414–445. MR 100789, DOI 10.1090/S0002-9947-1957-0100789-4
- Bent Fuglede, A commutativity theorem for normal operators, Proc. Nat. Acad. Sci. U.S.A. 36 (1950), 35–40. MR 32944, DOI 10.1073/pnas.36.1.35
- Paul R. Halmos, A Hilbert space problem book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0208368
- Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, Vol. 31, American Mathematical Society, Providence, R.I., 1957. rev. ed. MR 0089373
- Robert Moore, An asymptotic Fuglede theorem, Proc. Amer. Math. Soc. 50 (1975), 138–142. MR 370247, DOI 10.1090/S0002-9939-1975-0370247-7
- M. Rosenblum, On a theorem of Fuglede and Putnam, J. London Math. Soc. 33 (1958), 376–377. MR 99598, DOI 10.1112/jlms/s1-33.3.376
- Allen L. Shields, Weighted shift operators and analytic function theory, Topics in operator theory, Math. Surveys, No. 13, Amer. Math. Soc., Providence, R.I., 1974, pp. 49–128. MR 0361899
Additional Information
- © Copyright 1979 American Mathematical Society
- 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