Some refinements of numerical radius inequalities
DOI:
https://doi.org/10.37863/umzh.v72i10.6027Abstract
UDC 517.5
In this paper, we give some refinements for the second inequality in 12‖A‖≤w(A)≤‖A‖, where A∈B(H). In particular, if A is hyponormal by refining the Young inequality with the Kantorovich constant K(⋅,⋅), we show that w(A)≤12inf‖x‖=1ζ(x)‖|A|+|A∗|‖≤12‖|A|+|A∗|‖, where ζ(x)=K(⟨|A|x,x⟩⟨|A∗|x,x⟩,2)r, r=min{λ,1−λ} and 0≤λ≤1 . We also give a reverse for the classical numerical radius power inequality w(An)≤wn(A) for any operator A∈B(H) in the case when n=2.
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