Abstract
The theorem in [E. B. Davies, J. London Math. Soc. (2), 4, 435–436 (1972)] is extended. As a corollary, Kadison’s theorem on strong continuity of operator functions is refined.
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References
E. B. Davies, J. London Math. Soc. (2), 4 (1972), 435–436.
R. V. Kadison, Pacific J. Math., 26 (1968), 121–129.
M. Takesaki, Theory of operator algebras I, Springer-Verlag, Berlin-Heidelberg-New York, 1979.
S. Strătilă, Modular theory in operator algebras, Editura Academiei, Bucuresti; 1981.
O. E. Tikhonov, Izv. Vyssh. Uchebn. Zaved., Mat., 1987, No. 1, 77–79; English transl.: Sov. Math., 31:1 (1987), 110–114.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 41, No. 3, pp. 93–95, 2007
Original Russian Text Copyright © by O. E. Tikhonov
Supported by the Russian Foundation for Basic Research (project no. 05-01-00799).
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Tikhonov, O.E. On convergence of functions of normal operators in strong operator topology. Funct Anal Its Appl 41, 245–246 (2007). https://doi.org/10.1007/s10688-007-0022-y
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DOI: https://doi.org/10.1007/s10688-007-0022-y