INEQUALITIES FOR THE NORM AND NUMERICAL RADIUS FOR HILBERT 𝐶 * -MODULE OPERATORS
| Autor: | Mohsen Shah Hosseini, Baharak Moosavi |
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| Jazyk: | English<br />Russian |
| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Проблемы анализа, Vol 9 (27), Iss 2, Pp 87-96 (2020) |
| Druh dokumentu: | article |
| ISSN: | 2306-3424 2306-3432 |
| DOI: | 10.15393/j3.art.2020.7330 |
| Popis: | In this paper, we introduce some inequalities between the operator norm and the numerical radius of adjointable operators on Hilbert 𝐶*-module spaces. Moreover, we establish some new refinements of numerical radius inequalities for Hilbert space operators. More precisely, we prove that if 𝑇 ∈ 𝐵(𝐻) and min (︁‖𝑇 + 𝑇*‖^2/2, ‖𝑇 − 𝑇*‖^2/2)︁ ≤ max (︁inf_‖𝑥‖=1 ‖𝑇𝑥‖^2, inf_‖𝑥‖=1 ‖𝑇*𝑥‖^2)︁, then ‖𝑇‖≤ 2^(1/2)𝜔(𝑇); this is a considerable improvement of the classical inequality ‖𝑇‖≤ 2𝜔(𝑇). |
| Databáze: | Directory of Open Access Journals |
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