invertible positive operators, generalized weighted quasi-arithmetic means, Kubo-Ando means, nonlinear preservers
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.
Nagy, Gergő and Szokol, Patricia.
"Maps Preserving Norms of Generalized Weighted Quasi-arithmetic Means of Invertible Positive Operators",
Electronic Journal of Linear Algebra,
Volume 35, pp. 357-364.