Preserver Problems Related to Quasi-Arithmetic Means of Invertible Positive Operators

Transformations on Density Operators Preserving Generalised Entropy of a Convex Combination

“…For further results on preserver problems which are related to convex combinations, the interested reader is referred to [5,13,14].…”

On some isometries and other preservers

“…Proposition 3.1. (Gaál, Nagy [28]) Assume that f is bijective and let φ : P d → P d be a homomorphism with respect to each of the means M f,t for all t ∈ [0, 1]. Then there exists an integer k ∈ N, further we have matrices…”

“…Theorem 3.2. (Gaál, Nagy [28]) Suppose that | lim x→0 f (x)| = +∞ and that f (]0, +∞[) is any of the sets R, ]0, ∞[. Moreover, let t ∈]0, 1[ be a fixed real number and N(.)…”

“…Theorem 3.3. (Gaál, Nagy [28]) Suppose that f (x) = x λ (x > 0) with some scalar λ > 0 and let t ∈]0, 1[ be a fixed real number. Denote by .…”

“…Preserver problems related to quasi-arithmetic means (The results in this chapter are joint with Gergő Nagy and have been published in [28]. )…”