Abstract. Suppose a map φ on the set of positive definite matrices satisfies det(A + B) = det(φ(A) + φ(B)). Then we haveThrough this viewpoint, we show that φ is of the formfor some invertible matrix M with det(M * M ) = 1. We also characterize the map φ : S → S preserving the determinant of convex combinations in S by using similar method. Here S can be the set of complex matrices, positive definite matrices, symmetric matrices, and upper triangular matrices.
Being expected as a Banach space substitute of the orthogonal projections on Hilbert spaces, generalized n-circular projections also extend the notion of generalized bicontractive projections on JB*-triples. In this paper, we study some geometric properties of JB*-triples related to them. In particular, we provide some structure theorems of generalized n-circular projections on an often mentioned special case of JB*-triples, i.e., Hilbert C*-modules over abelian C*-algebras C 0 . /.
ABSTRACT. We describe the structure of all bijective maps on the cone of positive definite operators acting on a finite and at least twodimensional complex Hilbert space which preserve the quantum χ 2 α -divergence for some α ∈ [0, 1]. We prove that any such transformation is necessarily implemented by either a unitary or an antiunitary operator. Similar results concerning maps on the cone of positive semidefinite operators as well as on the set of all density operators are also derived.
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