| Title:
|
Spectral radius inequalities for positive commutators (English) |
| Author:
|
Zima, Mirosława |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
1 |
| Year:
|
2014 |
| Pages:
|
1-10 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We establish several inequalities for the spectral radius of a positive commutator of positive operators in a Banach space ordered by a normal and generating cone. The main purpose of this paper is to show that in order to prove the quasi-nilpotency of the commutator we do not have to impose any compactness condition on the operators under consideration. In this way we give a partial answer to the open problem posed in the paper by J. Bračič, R. Drnovšek, Y. B. Farforovskaya, E. L. Rabkin, J. Zemánek (2010). Inequalities involving an arbitrary commutator and a generalized commutator are also discussed. (English) |
| Keyword:
|
cone |
| Keyword:
|
positive operator |
| Keyword:
|
commutator |
| Keyword:
|
spectral radius |
| MSC:
|
47A10 |
| MSC:
|
47B47 |
| MSC:
|
47B65 |
| idZBL:
|
Zbl 06391470 |
| idMR:
|
MR3247438 |
| DOI:
|
10.1007/s10587-014-0077-x |
| . |
| Date available:
|
2014-09-29T09:25:55Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143941 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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|
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| . |
