| Title:
|
A note on the commutator of two operators on a locally convex space (English) |
| Author:
|
Kramar, Edvard |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
57 |
| Issue:
|
2 |
| Year:
|
2016 |
| Pages:
|
163-168 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Denote by $C$ the commutator $AB-BA$ of two bounded operators $A$ and $B$ acting on a locally convex topological vector space. If $AC-CA=0$, we show that $C$ is a quasinilpotent operator and we prove that if $AC-CA$ is a compact operator, then $C$ is a Riesz operator. (English) |
| Keyword:
|
locally convex space |
| Keyword:
|
commutator |
| Keyword:
|
nilpotent operator |
| Keyword:
|
compact operator |
| Keyword:
|
Riesz operator |
| MSC:
|
46A03 |
| MSC:
|
47B06 |
| MSC:
|
47B47 |
| idZBL:
|
Zbl 06604499 |
| idMR:
|
MR3513442 |
| DOI:
|
10.14712/1213-7243.2015.155 |
| . |
| Date available:
|
2016-07-05T15:03:05Z |
| Last updated:
|
2018-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145758 |
| . |
| Reference:
|
[1] Bonsall F.F., Duncan J.: Complete Normed Algebras.Springer, New York-Heidelberg-Berlin, 1973. Zbl 0271.46039, MR 0423029 |
| Reference:
|
[2] Chilana A.K.: Invariant subspaces for linear operators in locally convex spaces.J. London Math. Soc. 2 (1970), 493–503. Zbl 0198.45703, MR 0423095, 10.1112/jlms/2.Part_3.493 |
| Reference:
|
[3] Bračič J., Kuzma B.: Localizations of the Kleinecke-Shirokov Theorem.Oper. Matrices 1 (2007), 385–389. Zbl 1136.47025, MR 2344682, 10.7153/oam-01-22 |
| Reference:
|
[4] de Bruyn G.F.C.: Asymptotic properties of linear operators.Proc. London Math. Soc. 18 (1968), 405–427. Zbl 0172.16801, MR 0226442, 10.1112/plms/s3-18.3.405 |
| Reference:
|
[5] Kramar E.: On reducibility of sets of algebraic operators on locally convex spaces.Acta Sci. Math. (Szeged) 74 (2008), 729–742. Zbl 1199.47037, MR 2487942 |
| Reference:
|
[6] Lin C.S.: A note on the Kleinecke-Shirokov theorem and the Wintner-Halmos theorem.Proc. Amer. Math. Soc. 27 (1971), 529–530. MR 0284846, 10.1090/S0002-9939-1971-0284846-0 |
| Reference:
|
[7] Pietsch A.: Zur Theorie der $\sigma $-Transformationen in lokalkonvexen Vektorräumen.Math. Nachr. 21 (1960), 347–369. Zbl 0095.30903, MR 0123185, 10.1002/mana.19600210604 |
| Reference:
|
[8] Ruston A.F.: Operators with a Fredholm theory.J. London Math. Soc. 29 (1954), 318–326. Zbl 0055.10902, MR 0062345, 10.1112/jlms/s1-29.3.318 |
| . |
