Geodesic
On the asymptotic property of normal operators commutators in weak, strong and the strongest $B$-module operator typologies
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (1989), pp. 3-6.

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The asymptotic variant of Fugled–Putnam classic theorem is proved for the pair of limited normal operator acting in the Hilbert $B$-module $E$ in weak, strong and the strongest $B$-module operator topologies. Earlier, the asymptotic variants of the above mentioned theorem have been obtained in the papers [1–4]. 
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M. I. Karakhanyan. On the asymptotic property of normal operators commutators in weak, strong and the strongest $B$-module operator typologies. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (1989), pp. 3-6. http://geodesic.mathdoc.fr/item/UZERU_1989_1_a0/

[1] R. Moore, “An asymptotic Fuglede theorem”, Proc. Amer. Math. Soc., 50 (1975), 138–148 | DOI | MR

[2] E. A. Gorin, M. I. Karakhanyan, “Asimptoticheskii variant teoremy Fuglida–Putnama o kommutatorakh dlya elementov banakhovykh algebr”, Matem. zametki, 22:2 (1977), 179–188 | MR | Zbl

[3] M. I. Karakhanyan, “Asimptoticheskii variant teoremy Fuglida-Putnama o kommutatorakh lineinykh ogranichennykh operatorov v silnoi i slaboi operatornykh topologiyakh”, DAN Arm. SSR, 73:5 (1981), 265–268 | Zbl

[4] D. D. Rogers, “On Fuglede’s theorem and operator topologies”, Proc. Amer. Math. Soc., 75 (1979), 32–36 | MR | Zbl

[5] W. L. Pashke, “Pashke Inner product modules over $B^{\ast}$-algebras”, Trans. of the Amer. Math. Soc., 182 (1973), 443–468 | MR