An extension of the weighted geometric mean in unital JB-algebras

2023/06/11 by Ghazanfari, Amir Ghasem, Malekinejad, Somayeh
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2306.06685

Abstract

Let A be a unital JB-algebra and A,~B\inA, we extend the weighted geometric mean A\sharp_r B, from r∈ [0,1] to r∈ (-1, 0)∪(1, 2). We will notice that many results will be reversed when the domain of r change from [0,1] to (-1,0) or (1,2). We investigate some property of A\sharp_r B for such quantities of r, such as we show that A\sharp_r B is separately operator convex with respect to A, B. We also introduce the Heinz and Heron means for unital JB-algebras and give some famous inequalities involving them.

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