| Title:
|
On a Kleinecke-Shirokov theorem (English) |
| Author:
|
Lauric, Vasile |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
71 |
| Issue:
|
3 |
| Year:
|
2021 |
| Pages:
|
817-822 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Kleinecke-Shirokov theorem |
| Keyword:
|
generalized commutator |
| MSC:
|
47B10 |
| MSC:
|
47B20 |
| MSC:
|
47B47 |
| idZBL:
|
07396199 |
| idMR:
|
MR4295247 |
| DOI:
|
10.21136/CMJ.2021.0103-20 |
| . |
| Date available:
|
2021-08-02T08:07:36Z |
| Last updated:
|
2023-10-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149058 |
| . |
| Reference:
|
[1] Abdessemed, A., Davies, E. B.: Some commutator estimates in the Schatten classes.J. Lond. Math. Soc., II. Ser. 39 (1989), 299-308. Zbl 0692.47009, MR 0991663, 10.1112/jlms/s2-39.2.299 |
| Reference:
|
[2] Ackermans, S. T. M., Eijndhoven, S. J. L. van, Martens, F. J. L.: On almost commuting operators.Indag. Math. 45 (1983), 385-391. Zbl 0573.47024, MR 0731821, 10.1016/S1385-7258(83)80015-8 |
| Reference:
|
[3] Kleinecke, D. C.: On operator commutators.Proc. Am. Math. Soc. 8 (1957), 535-536. Zbl 0079.12904, MR 0087914, 10.1090/S0002-9939-1957-0087914-4 |
| Reference:
|
[4] Shirokov, F. V.: Proof of a conjecutre of Kaplansky.Usp. Mat. Nauk 11 (1956), 167-168 Russian. Zbl 0070.34201, MR 0087913 |
| Reference:
|
[5] Shulman, V.: Some remarks on the Fuglede-Weiss theorem.Bull. Lond. Math. Soc. 28 (1996), 385-392. Zbl 0892.47007, MR 1384827, 10.1112/blms/28.4.385 |
| Reference:
|
[6] Shulman, V., Turowska, L.: Operator synthesis. II: Individual synthesis and linear operator equations.J. Reine Angew. Math. 590 (2006), 143-187. Zbl 1094.47054, MR 2208132, 10.1515/CRELLE.2006.007 |
| . |
