NEW NORM INEQUALITIES FOR COMMUTATORS OF HILBERT SPACE OPERATORS
New norm inequalities for commutators of Hilbert space operators are given. Among other inequalities, it is shown that if $A, B \in \mathbb{B}(\mathbb{H})$ and there exists a real number $z_0$, such that $||A-z_0I|| = D_A$, then \[ ||AB \pm BA^*|| \le 2D_A||B||, \] where $D_A = \underset{\l...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Petrozavodsk State University
2025-02-01
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| Series: | Проблемы анализа |
| Subjects: | |
| Online Access: | https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=16510&lang=en |
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| Summary: | New norm inequalities for commutators of Hilbert space operators are given. Among other inequalities, it is shown that if $A, B \in \mathbb{B}(\mathbb{H})$ and there exists a real number $z_0$, such that $||A-z_0I|| = D_A$, then
\[
||AB \pm BA^*|| \le 2D_A||B||,
\]
where $D_A = \underset{\lambda \in \mathbb{C}}{inf} ||A - \lambda I||$. In particular, under some conditions, we prove that
\[
||AB|| \le D_A||B||,
\]
which is an improvement of submultiplicative norm inequality. Also, we prove several numerical radius inequalities for products of two Hilbert space operators. |
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| ISSN: | 2306-3424 2306-3432 |