Bhunia, P (2024) Improved bounds for the numerical radius via polar decomposition of operators. In: Linear Algebra and Its Applications, 683 . pp. 31-45.
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Abstract
Using the polar decomposition of a bounded linear operator A defined on a complex Hilbert space, we obtain several numerical radius inequalities of the operator A, which generalize and improve the earlier related ones. Among other bounds, we show that if w(A) is the numerical radius of A, then Formula presented for all t�0,1. Also, we obtain some upper bounds for the numerical radius involving the spectral radius and the Aluthge transform of operators. It is shown that Formula presented where A�=|A|1/2U|A|1/2 is the Aluthge transform of A and A=U|A| is the polar decomposition of A. Other related results are also provided. © 2023 Elsevier Inc.
| Item Type: | Journal Article |
|---|---|
| Publication: | Linear Algebra and Its Applications |
| Publisher: | Elsevier Inc. |
| Additional Information: | The copyright for this article belongs to author. |
| Keywords: | Matrix algebra, Aluthge transforms; Bounded linear operators; Inequality; Numerical radius; Operator norm; Polar decompositions; Spectral radius; Upper Bound, Mathematical operators |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 28 Feb 2024 11:15 |
| Last Modified: | 28 Feb 2024 11:15 |
| URI: | https://eprints.iisc.ac.in/id/eprint/83702 |
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