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New Inequalities for Numerical Radius of Hilbert Space Operator And New Bounds For The Zeros Of Polynomials

It is shown that if Ar does not converge to the zero operator on a complex Hilbert space for some r ≥ 1, then And if there exists 1 such that Ar is a zero operator on a complex Hilbert space for all r ≥ 2, then where W(.) and ||.|| are the numerical radius and the usual operator norm, respectively. Also, the previous inequalities are better than any other classical inequalities.