By taking into account that the computation of the numerical radius is an optimization problem, we prove, in this paper, several refinements of the numerical radius inequalities for Hilbert space operators. It is shown, among other inequalities, that if A is a bounded linear operator on a complex Hilbert space, then ω(A)≤½√(|| |A|2+|A*|2||+|| |A| |A*|+|A*| |A| ||), where ω(A), ||A||, and |A| are the numerical radius, the usual operator norm, and the absolute value of A, respectively. This inequality provides a refinement of an earlier numerical radius inequality due to Kittaneh, namely, ω(A)≤½(||A||+||A2||)½. Some related inequalities are also discussed.
Pouladi Najafabadi, F., Moradi, H. (2021). Advanced Refinements of Numerical Radius Inequalities. International Journal of Mathematical Modelling & Computations, 11(4 (Fall)), -. doi: 10.30495/ijm2c.2021.684828
MLA
Farzaneh Pouladi Najafabadi; Hamid Reza Moradi. "Advanced Refinements of Numerical Radius Inequalities". International Journal of Mathematical Modelling & Computations, 11, 4 (Fall), 2021, -. doi: 10.30495/ijm2c.2021.684828
HARVARD
Pouladi Najafabadi, F., Moradi, H. (2021). 'Advanced Refinements of Numerical Radius Inequalities', International Journal of Mathematical Modelling & Computations, 11(4 (Fall)), pp. -. doi: 10.30495/ijm2c.2021.684828
VANCOUVER
Pouladi Najafabadi, F., Moradi, H. Advanced Refinements of Numerical Radius Inequalities. International Journal of Mathematical Modelling & Computations, 2021; 11(4 (Fall)): -. doi: 10.30495/ijm2c.2021.684828
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