## 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].

### MSC:

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

### Keywords:

numerical radius; operator norm; inequality; involution operator

### Citations:

Zbl 1113.15302; Zbl 1072.47004
Full Text:

### References:

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