Numerical radius inequalities of sectorial matrices

Bhunia, P and Paul, K and Sen, A (2023) Numerical radius inequalities of sectorial matrices. In: Annals of Functional Analysis, 14 (3).

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Abstract

We obtain several upper and lower bounds for the numerical radius of sectorial matrices. We also develop several numerical radius inequalities of the sum, product and commutator of sectorial matrices. The inequalities obtained here are sharper than the existing related inequalities for general matrices. Among many other results we prove that if A is an n× n complex matrix with the numerical range W(A) satisfying W(A)⊆{re±iθ:θ1≤θ≤θ2}, where r> 0 and θ1, θ2∈ [ 0 , π/ 2 ] , then (i)w(A)≥cscγ2‖A‖+cscγ2|‖ℑ(A)‖-‖ℜ(A)‖|,and(ii)w2(A)≥csc2γ4‖AA∗+A∗A‖+csc2γ2|‖ℑ(A)‖2-‖ℜ(A)‖2|, where γ= max { θ2, π/ 2 - θ1} . We also prove that if A, B are sectorial matrices with sectorial index γ∈ [ 0 , π/ 2 ) and they are double commuting, then w(AB) ≤ (1 + sin 2γ) w(A) w(B).

Item Type:	Journal Article
Publication:	Annals of Functional Analysis
Publisher:	Birkhauser
Additional Information:	The copyright for this article belongs to the Author.
Keywords:	Accretive matrix; Numerical radius; Numerical range; Sectorial matrix.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	28 Jul 2023 06:45
Last Modified:	28 Jul 2023 06:45
URI:	https://eprints.iisc.ac.in/id/eprint/82573

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