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An application of the Putnam-Fuglede theorem to normal products of self-adjoint operators

Author(s): Hichem M. Mortad
Journal: Proc. Amer. Math. Soc. 131 (2003), 3135-3141.
MSC (2000): Primary 47B15, 47B25
Posted: January 2, 2003
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Abstract: We prove that if we have two self-adjoint operators (bounded or not) and if their product is normal, then it is self-adjoint provided a certain condition is satisfied.

References:

1.: E. Albrecht, P. G. Spain, When Products of Selfadjoints Are Normal, Proc. American Math. Soc., 128/8 (2000) 2509-2511. MR 2000m:46001
2.: J. B. Conway, A Course in Functional Analysis, Springer, 1990 (2nd edition). MR 91e:46001
3.: B. Fuglede, A Commutativity Theorem For Normal Operators, Proc. National Acad. Sci., 36 (1950) 35-40. MR 13:253d
4.: C. R. Putnam, On Normal Operators in Hilbert Space, Amer. J. Math., 73 (1951) 357-362. MR 12:717f
5.: M. Reed, B. Simon, Methods of Modern Mathematical Physics (Vol.1, Functional Analysis), Acad. Press, 1972. MR 58:12429a


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