Geodesic
On a Kleinecke-Shirokov theorem
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 3, pp. 817-822
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We prove that for normal operators $N_1, N_2\in \mathcal {L(H)},$ the generalized commutator $[N_1, N_2; X]$ approaches zero when $[N_1,N_2; [N_1, N_2; X]]$ tends to zero in the norm of the Schatten-von Neumann class $\mathcal {C}_p$ with $p>1$ and $X$ varies in a bounded set of such a class.
We prove that for normal operators $N_1, N_2\in \mathcal {L(H)},$ the generalized commutator $[N_1, N_2; X]$ approaches zero when $[N_1,N_2; [N_1, N_2; X]]$ tends to zero in the norm of the Schatten-von Neumann class $\mathcal {C}_p$ with $p>1$ and $X$ varies in a bounded set of such a class.
DOI : 10.21136/CMJ.2021.0103-20
Classification : 47B10, 47B20, 47B47
Keywords: Kleinecke-Shirokov theorem; generalized commutator 
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Lauric, Vasile. On a Kleinecke-Shirokov theorem. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 3, pp. 817-822. doi: 10.21136/CMJ.2021.0103-20

[1] Abdessemed, A., Davies, E. B.: Some commutator estimates in the Schatten classes. J. Lond. Math. Soc., II. Ser. 39 (1989), 299-308. | DOI | MR | JFM

[2] Ackermans, S. T. M., Eijndhoven, S. J. L. van, Martens, F. J. L.: On almost commuting operators. Indag. Math. 45 (1983), 385-391. | DOI | MR | JFM

[3] Kleinecke, D. C.: On operator commutators. Proc. Am. Math. Soc. 8 (1957), 535-536. | DOI | MR | JFM

[4] Shirokov, F. V.: Proof of a conjecutre of Kaplansky. Usp. Mat. Nauk 11 (1956), 167-168 Russian. | MR | JFM

[5] Shulman, V.: Some remarks on the Fuglede-Weiss theorem. Bull. Lond. Math. Soc. 28 (1996), 385-392. | DOI | MR | JFM

[6] Shulman, V., Turowska, L.: Operator synthesis. II: Individual synthesis and linear operator equations. J. Reine Angew. Math. 590 (2006), 143-187. | DOI | MR | JFM

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