Maps Preserving Norms of Generalized Weighted Quasi-arithmetic Means of Invertible Positive Operators

Author:

Nagy Gergő,Szokol Patricia

Abstract

In this paper, the problem of describing the structure of transformations leaving norms of generalized weighted quasi-arithmetic means of invertible positive operators invariant is discussed. In a former result of the authors, this problem was solved for weighted quasi-arithmetic means, and here the corresponding result is generalized by establishing its solution under certain mild conditions. It is proved that in a quite general setting, generalized weighted quasi-arithmetic means on self-adjoint operators are not monotone in their variables which is an interesting property. Moreover, the relation of these means with the Kubo-Ando means is investigated and it is shown that the common members of the classes of these types of means are weighted arithmetic means.

Publisher

University of Wyoming Libraries

Subject

Algebra and Number Theory

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