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An asymptotic Fuglede theorem
Author:
Robert Moore
Journal:
Proc. Amer. Math. Soc. 50 (1975), 138-142
MSC:
Primary 47B15; Secondary 46L15
MathSciNet review:
0370247
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Abstract: The main result is that if an operator  on Hilbert space ``almost'' commutes with a normal operator  , then  almost commutes with  as well. The Theorem is then extended to a Putnam-like version which states that if  almost intertwines two normal operators, then it almost intertwines continuous functions of those operators.
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J. Bastian and K.
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asymptotic properties of normal operators, Proc. Amer. Math. Soc. 42 (1974), 475–479. MR 0380491
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S.
K. Berberian, Note on a theorem of Fuglede and
Putnam, Proc. Amer. Math. Soc. 10 (1959), 175–182. MR 0107826
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P.
R. Halmos, What does the spectral theorem say?, Amer. Math.
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E. Johnson and J.
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Math. 58 (1975), no. 1, 105–122. MR 0380490
(52 #1390)
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M.
Rosenblum, On a theorem of Fuglede and Putnam, J. London Math.
Soc. 33 (1958), 376–377. MR 0099598
(20 #6037)
- [1]
- J. J. Bastian and K. J. Harrison, Subnormal weighted shifts and asymptotic properties of normal operators, 1973 (preprint). MR 0380491 (52:1391)
- [2]
- S. K. Berberian, Note on a theorem of Fuglede and Putnam, Proc. Amer. Math. Soc. 10 (1959), 175-182. MR 21 #6548. MR 0107826 (21:6548)
- [3]
- P. R. Halmos, What does the spectral theorem say? Amer. Math. Monthly 70 (1963), 241-247. MR 27 #595. MR 0150600 (27:595)
- [4]
- B. E. Johnson and J. P. Williams, The range of a normal derivation, Pacific J. Math. (to appear). MR 0380490 (52:1390)
- [5]
- Marvin Rosenblum, On a theorem of Fuglede and Putnam, J. London Math. Soc. 33 (1958), 376-377. MR 20 #6037. MR 0099598 (20:6037)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1975-0370247-7
PII:
S 0002-9939(1975)0370247-7
Keywords:
Normal operator,
Fuglede theorem,
spectral measure
Article copyright:
© Copyright 1975 American Mathematical Society
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