Inequalities Involving the Numerical Radius

Charles R. Johnson; I. M. Spitkovsky; S. Gottlieb

doi:10.1080/03081089408818310

Inequalities Involving the Numerical Radius

Charles R. Johnson, I. M. Spitkovsky, S. Gottlieb

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

For the classical numerical radius r(A) of an n-by n real or complex matrix A, we consider inequalities of the following two types: r(f(A)) ≤ f(r(A)); and r(f(A)g(A)) ≤ r(f(A))r(g(A)) in which f and g are polynomials. In the latter case, the event in which f and g are simple powers is of special interest. We present a variety of particular results depending upon the dimension n and the classification of A or the polynomials. A number of natural questions remain open

Original language	English (US)
Pages (from-to)	13-24
Number of pages	12
Journal	Linear and Multilinear Algebra
Volume	37
Issue number	1-3
DOIs	https://doi.org/10.1080/03081089408818310
State	Published - Jun 1 1994

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/03081089408818310

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abstract = "For the classical numerical radius r(A) of an n-by n real or complex matrix A, we consider inequalities of the following two types: r(f(A)) ≤ f(r(A)); and r(f(A)g(A)) ≤ r(f(A))r(g(A)) in which f and g are polynomials. In the latter case, the event in which f and g are simple powers is of special interest. We present a variety of particular results depending upon the dimension n and the classification of A or the polynomials. A number of natural questions remain open",

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AU - Gottlieb, S.

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N2 - For the classical numerical radius r(A) of an n-by n real or complex matrix A, we consider inequalities of the following two types: r(f(A)) ≤ f(r(A)); and r(f(A)g(A)) ≤ r(f(A))r(g(A)) in which f and g are polynomials. In the latter case, the event in which f and g are simple powers is of special interest. We present a variety of particular results depending upon the dimension n and the classification of A or the polynomials. A number of natural questions remain open

AB - For the classical numerical radius r(A) of an n-by n real or complex matrix A, we consider inequalities of the following two types: r(f(A)) ≤ f(r(A)); and r(f(A)g(A)) ≤ r(f(A))r(g(A)) in which f and g are polynomials. In the latter case, the event in which f and g are simple powers is of special interest. We present a variety of particular results depending upon the dimension n and the classification of A or the polynomials. A number of natural questions remain open

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Inequalities Involving the Numerical Radius

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