An asymptotic Fuglede theorem

Moore, Robert

doi:10.1090/S0002-9939-1975-0370247-7

An asymptotic Fuglede theorem
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by Robert Moore

Proc. Amer. Math. Soc. 50 (1975), 138-142

DOI: https://doi.org/10.1090/S0002-9939-1975-0370247-7

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Abstract:

The main result is that if an operator $B$ on Hilbert space “almost” commutes with a normal operator $N$, then $B$ almost commutes with ${N^\ast }$ as well. The Theorem is then extended to a Putnam-like version which states that if $B$ almost intertwines two normal operators, then it almost intertwines continuous functions of those operators.

References

J. J. Bastian and K. J. Harrison, Subnormal weighted shifts and asymptotic properties of normal operators, Proc. Amer. Math. Soc. 42 (1974), 475–479. MR 380491, DOI 10.1090/S0002-9939-1974-0380491-X
S. K. Berberian, Note on a theorem of Fuglede and Putnam, Proc. Amer. Math. Soc. 10 (1959), 175–182. MR 107826, DOI 10.1090/S0002-9939-1959-0107826-9
P. R. Halmos, What does the spectral theorem say?, Amer. Math. Monthly 70 (1963), 241–247. MR 150600, DOI 10.2307/2313117
B. E. Johnson and J. P. Williams, The range of a normal derivation, Pacific J. Math. 58 (1975), no. 1, 105–122. MR 380490
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