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Numerical Radius Inequalities for Sums and Products of Operators

DOI: 10.4236/alamt.2019.93003, PP. 35-42

Keywords: Numeriacl Radius, Operator Norm, Operator Matrix, Inequality, Equality, Offdiagonal Part

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Abstract:

A numerical radius inequality due to Shebrawi and Albadawi says that: If Ai, Bi, Xi are bounded operators in Hilbert space, i = 1,2,..., n , and f,g be nonnegative continuous functions on [0, ∞) satisfying the relation f(t)g(t) = t (t∈[0, ∞)), then \"\" for all r≥1. We give sharper numerical radius inequality which states that: If Ai, Bi, Xi are bounded operators in Hilbert space, i = 1,2,..., n , and f,g be nonnegative continuous functions on [0, ∞) satisfying the relation f(t)g(t) = t (t∈[0, ∞)), then \"\"?where \"\". Moreover, we give many numerical radius inequalities which are sharper than related inequalities proved recently, and several applications are given.

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