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A geometric approach to numerical radius inequalities
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NSTL
Elsevier
? 2022 Elsevier Inc.In this article we present new numerical radius inequalities for sectorial matrices, and their analogues. For example, we show that if A is a sectorial matrix with sectorial index [Formula presented], then [Formula presented] where w(A) is the numerical radius of A. The significance of this result is the geometric meaning of the obtained inequality. In particular, we will show how this interpolates some well known inequalities in the literature, in a way that depends on the angle of the sector that contains the numerical range of the sectorial matrix A. Many other interpolating inequalities will be presented to show how the ratio [Formula presented] depends mainly on the angle of the sector that contains the numerical range of the matrix A. Our discussion will lead to a new vision about those matrices which contain the origin in the interior of their numerical ranges.
Accretive matricesGeometry of the numerical rangeInterpolating inequalitiesNumerical radius
Abu Sammour S.、Kittaneh F.、Sababheh M.
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Department of Mathematics The University of Jordan
NSTL
Elsevier
