Extensions of the arithmetic–geometric means and Young's norm inequalities to accretive operators, with applications

Abstract

If (Formula presented.) are normal accretive operators, (Formula presented.) and Φ is a s.n. function, we proved that (Formula presented.) (Formula presented.) Let (Formula presented.) and Φ be a s.n. function. If (Formula presented.) then we have the following generalization of Young's norm inequality in Jocić [Cauchy–Schwarz norm inequalities for weak*-integrals of operator valued functions. J Funct Anal. 2005;218:318–346], Corollary 4.1 (Formula presented.) Various examples and applications of the obtained norm inequalities are also presented, including those related to the Heinz and Heron means and Zhan inequalities.