Numerical Radius Inequalities for Sums and Products of Operators

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DOI: 10.4236/alamt.2019.93003    798 Downloads   1,738 Views  
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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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Audeh, W. (2019) Numerical Radius Inequalities for Sums and Products of Operators. Advances in Linear Algebra & Matrix Theory, 9, 35-42. doi: 10.4236/alamt.2019.93003.

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