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Further refinements of generalized numerical radius inequalities for Hilbert space operators

Monire Hajmohamadi, Rahmatollah Lashkaripour and Mojtaba Bakherad

Abstract

In this paper, we show some refinements of generalized numerical radius inequalities involving the Young and Heinz inequality. In particular, we present

wpp(A1*T1B1,,An*TnBn)n1-1r21ri=1n[Bi*f2(|Ti|)Bi]rp+[Ai*g2(|Ti*|)Ai]rp1r-infx=1η(x),

where Ti,Ai,Bi𝔹()(1in), f and g are nonnegative continuous functions on [0,) satisfying f(t)g(t)=t for all t[0,), p,r1, N, and

η(x)=12i=1nj=1N((Ai*g2(|Ti*|)Ai)px,x2j-1-kj(Bi*f2(|Ti|)Bi)px,xkj2j
-(Bi*f2(|Ti|)Bi)px,xkj+1(Ai*g2(|Ti*|)Ai)px,x2j-1-kj-12j)2.

MSC 2010: 47A12; 47A63; 47A30

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Received: 2016-09-29
Accepted: 2018-05-21
Published Online: 2019-05-07
Published in Print: 2021-02-01

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