Upper and lower bounds for the numerical radius with an application to involution operators. (English) Zbl 1339.47007

Using the numerical radius of \(A^2\), the authors improve the upper bound of the numerical radius of \(A\) which was obtained by the second author [Stud. Math. 158, No. 1, 11–17 (2003; Zbl 1113.15302); Stud. Math. 168, No. 1, 73–80 (2005; Zbl 1072.47004)]. Also, considering the infimum of the numerical range of \(A\), a lower bound for numerical radius of \(A\) is presented which is sharper than the one in [Zbl 1072.47004].


47A12 Numerical range, numerical radius
47A63 Linear operator inequalities
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