Unexpected relations which characterize operator means
Unexpected relations which characterize operator means
We give some characterizations of self-adjointness and symmetricity of operator monotone functions by using the Barbour transform <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f right-arrow from bar StartFraction t plus f Over 1 plus f EndFraction"> <mml:semantics> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo stretchy="false">↦<!-- ↦ --></mml:mo> <mml:mfrac> <mml:mrow> <mml:mi>t</mml:mi> <mml:mo>+</mml:mo> <mml:mi>f</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> …