%0 Journal Article
%T Numerical Radius Inequalities for Sums and Products of Operators
%A Wasim Audeh
%J Advances in Linear Algebra & Matrix Theory
%P 35-42
%@ 2165-3348
%D 2019
%I Scientific Research Publishing
%R 10.4236/alamt.2019.93003
%X <p>
	A numerical radius inequality due to Shebrawi and Albadawi says that: If <i>A<sub>i</sub></i>, <i>B<sub>i</sub></i>, <i>X<sub>i</sub></i> are bounded operators in Hilbert space, <i>i</i> = 1,2,..., n , and <i>f,g</i> be nonnegative continuous functions on [0, <span style=\"font-size:10.0pt;font-family:;\" \"=\"\">¡Þ) </span>satisfying the relation <i>f(t)g(t) = t</i> (<i>t</i>¡Ê[0, ¡Þ)), then <img src=\"Edit_e4155032-1750-42d4-af3e-abddd461ced8.png\" width=\"300\" height=\"30\" alt=\"\" /> for all <i>r</i>¡Ý1. We give sharper numerical radius inequality which states that: If <i style=\"white-space:normal;\">A<sub>i</sub></i><span style=\"white-space:normal;\">, </span><i style=\"white-space:normal;\">B<sub>i</sub></i><span style=\"white-space:normal;\">, </span><i style=\"white-space:normal;\">X<sub>i</sub></i> are bounded operators in Hilbert space, <i>i</i> = 1,2,..., n , and <i>f,g</i> be nonnegative continuous functions on [0, <span style=\"font-size:10.0pt;font-family:;\" \"=\"\">¡Þ) </span>satisfying the relation <i>f(t)g(t) = t</i> (<i>t</i>¡Ê[0, ¡Þ)), then <img src=\"Edit_441ec382-fafc-4d04-8960-97802962a498.png\" width=\"300\" height=\"30\" alt=\"\" />&nbsp;where <img src=\"Edit_f8b9782f-c5f0-4724-8627-fa5baf4230d3.png\" width=\"350\" height=\"35\" alt=\"\" />. Moreover, we give many numerical radius inequalities which are sharper than related inequalities proved recently, and several applications are given.
</p>
%K Numeriacl Radius
%K Operator Norm
%K Operator Matrix
%K Inequality
%K Equality
%K Offdiagonal Part
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=93598