Startseite Further refinements of generalized numerical radius inequalities for Hilbert space operators
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Further refinements of generalized numerical radius inequalities for Hilbert space operators

  • Monire Hajmohamadi , Rahmatollah Lashkaripour EMAIL logo und Mojtaba Bakherad
Veröffentlicht/Copyright: 7. Mai 2019
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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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