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
Full-text PDF
Abstract | References | Similar Articles | Additional Information
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 and
in D imply
in E. An example is given to show that D depends on N as well as E.
- [1] E. Bishop, Spectral theory for operators on a Banach space, Trans. Amer. Math. Soc. 86 (1957), 414-445. MR 0100789 (20:7217)
- [2] B. Fuglede, A commutativity theorem for normal operators, Proc. Nat. Acad. Sci. U.S.A. 36 (1950), 35-40. MR 0032944 (11:371c)
- [3] P. R. Halmos, A Hilbert space problem book, Van Nostrand, Princeton, N. J., 1967. MR 0208368 (34:8178)
- [4] E. Hille and R. S. Phillips, Functional analysis and semi-groups, Amer. Math. Soc. Colloq. Publ., vol. 31, Amer. Math. Soc., Providence, R. I., 1957. MR 0089373 (19:664d)
- [5] R. L. Moore, An asymptotic Fuglede theorem, Proc. Amer. Math. Soc. 50 (1975), 138-142. MR 0370247 (51:6474)
- [6] M. Rosenblum, On a theorem of Fuglede and Putnam, J. London Math. Soc. 33 (1958), 376-377. MR 0099598 (20:6037)
- [7] A. L. Shields, Weighted shift operators and analytic function theory, Math. Surveys, No. 13, Amer. Math. Soc., Providence, R. I., 1974, pp. 49-128. MR 0361899 (50:14341)
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B15
Retrieve articles in all journals with MSC: 47B15
Additional Information
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