Numerical radius inequalities and estimation of zeros of polynomials

Bhunia, P and Jana, S and Paul, K (2023) Numerical radius inequalities and estimation of zeros of polynomials. [Preprint]

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Abstract

Let A be a bounded linear operator defined on a complex Hilbert space and let | A | = (A A) 1 2 |A|=(Aâ��A)\frac12. Among other refinements of the well-known numerical radius inequality w 2(A) â�¤ 1 2â�¥A A + AA â�� â�¥, we show that w 2(A) â�¤ 1 4w 2(| A| + i |A â�� |) + 1 8â�¥| A | 2 + | A â�� | 2 â�¥+ 1 4w(| A || A â�� |) â�¤ 1 2â�¥A A + AA â�� â�¥. w. Also, we develop inequalities involving the numerical radius and the spectral radius for the sum of the product operators, from which we derive the inequalities w p(A) â�¤ 1 2w(| A | p + i| A â�� | p) â�¤ â�¥A â�¥p wp(A)≤\frac1\sqrt2w(|A|p+\rm i|Aâ��|p)≤\|A\|p for all p â�¥ 1 p\geq 1. Further, we derive new bounds for the zeros of complex polynomials. © 2023 Walter de Gruyter GmbH, Berlin/Boston.

Item Type:	Preprint
Publication:	Georgian Mathematical Journal
Publisher:	Walter de Gruyter GmbH
Additional Information:	The copyright for this article belongs to authors.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	14 Dec 2024 00:16
Last Modified:	14 Dec 2024 00:16
URI:	http://eprints.iisc.ac.in/id/eprint/85422

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