A Numerical Radius Version of the Arithmetic-Geometric Mean of Operators

作者：Sheikhhosseini Alemeh^*

来源：Filomat, 2016, 30(8): 2139-2145.

DOI：10.2298/FIL1608139S

• Geometric mean
• Inequalities
• Numerical radius
• Operator norm

In this paper, we obtain some numerical radius inequalities for operators, in particular for positive definite operators A, B a numerical radius and some operator norm versions for arithmetic-geometric mean inequality are obtained, respectively as
omega(2)(A#B) <= omega(A(2) + B-2/2) - 1/2(parallel to x parallel to=1)inf delta(x),
where delta(x) = <(A - B)x, x >(2), and
parallel to A parallel to parallel to B parallel to <= 1/2 (parallel to A(2)parallel to + parallel to B-2 parallel to) - 1/2(parallel to x parallel to=parallel to y parallel to=1)inf delta(x, y),
where, delta(x, y) = (< Ay, y > - << Bx, x >)(2).

• 出版日期2016