Document Zbl 0458.47020

An extension of the Fuglede-Putnam theorem to subnormal operators using a Hilbert-Schmidt norm inequality. (English) Zbl 0458.47020

Proc. Am. Math. Soc. 81, 240-242 (1981).

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MSC:

47B20	Subnormal operators, hyponormal operators, etc.
47B10	Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
47B15	Hermitian and normal operators (spectral measures, functional calculus, etc.)
47B47	Commutators, derivations, elementary operators, etc.

Keywords:

subnormal operator; hyponormal operator; Hilbert-Schmidt class

Citations:

Zbl 0414.47024

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Full Text: DOI

References:

[1]	S. K. Berberian, Note on a theorem of Fuglede and Putnam, Proc. Amer. Math. Soc. 10 (1959), 175 – 182. · Zbl 0092.32004
[2]	S. K. Berberian, Extensions of a theorem of Fuglede and Putnam, Proc. Amer. Math. Soc. 71 (1978), no. 1, 113 – 114. · Zbl 0388.47019
[3]	Takayuki Furuta, On relaxation of normality in the Fuglede-Putnam theorem, Proc. Amer. Math. Soc. 77 (1979), no. 3, 324 – 328. · Zbl 0388.47018
[4]	Paul R. Halmos, Shifts on Hilbert spaces, J. Reine Angew. Math. 208 (1961), 102 – 112. · Zbl 0107.09802 · doi:10.1515/crll.1961.208.102
[5]	Paul R. Halmos, A Hilbert space problem book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. · Zbl 0144.38704
[6]	C. R. Putnam, On normal operators in Hilbert space, Amer. J. Math. 73 (1951), 357 – 362. · Zbl 0042.34501 · doi:10.2307/2372180
[7]	M. Rosenblum, On a theorem of Fuglede and Putnam, J. London Math. Soc. 33 (1958), 376 – 377. · Zbl 0081.11902 · doi:10.1112/jlms/s1-33.3.376
[8]	Gary Weiss, The Fuglede commutativity theorem modulo operator ideals, Proc. Amer. Math. Soc. 83 (1981), no. 1, 113 – 118. · Zbl 0478.47004
[9]	-, Fuglede’s commutativity theorem modulo the Hilbert-Schmidt class and generating functions for matrix operators. II (to appear).

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