| Title:
|
Inequalities between the sum of powers and the exponential of sum of positive and commuting selfadjoint operators (English) |
| Author:
|
Bendoukha, Berrabah |
| Author:
|
Bendahmane, Hafida |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
47 |
| Issue:
|
4 |
| Year:
|
2011 |
| Pages:
|
257-262 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let ${\mathcal{B}}({\mathcal{H}})$ be the set of all bounded linear operators acting in Hilbert space ${\mathcal{H}}$ and ${\mathcal{B}}^{+}({\mathcal{H}})$ the set of all positive selfadjoint elements of ${\mathcal{B}}({\mathcal{H}})$. The aim of this paper is to prove that for every finite sequence $(A_{i})_{i=1}^{n}$ of selfadjoint, commuting elements of ${\mathcal{B}}^{+}({\mathcal{H}})$ and every natural number $p\ge 1$, the inequality
\[ \frac{e^{p}}{p^{p}}\Big (\sum _{i=1}^{n}A_{i}^{p}\Big )\le \exp \Big (\sum _{i=1}^{n}A_{i}\Big )\,, \]
holds. (English) |
| Keyword:
|
commuting operators |
| Keyword:
|
positive selfadjoint operator |
| Keyword:
|
spectral representation |
| MSC:
|
47A30 |
| MSC:
|
47B60 |
| idZBL:
|
Zbl 1249.47019 |
| idMR:
|
MR2876948 |
| . |
| Date available:
|
2011-12-16T15:13:03Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141774 |
| . |
| Reference:
|
[1] Akhiezer, N. I., Glasman, I. M.: Theory of linear operators in Hilbert space.Tech. report, Vyshcha Shkola, Kharkov, 1977, English transl. Pitman (APP), 1981. MR 0486990 |
| Reference:
|
[2] Belaidi, B., Farissi, A. El, Latreuch, Z.: Inequalities between sum of the powers and the exponential of sum of nonnegative sequence.RGMIA Research Collection, 11 (1), Article 6, 2008. |
| Reference:
|
[3] Qi, F.: Inequalities between sum of the squares and the exponential of sum of nonnegative sequence.J. Inequal. Pure Appl. Math. 8 (3) (2007), 1–5, Art. 78. MR 2345933 |
| Reference:
|
[4] Weidman, J.: Linear operators in Hilbert spaces.New York, Springer, 1980. MR 0566954 |
| . |
