Spectral isometries on non-simple C*-algebras

We prove that unital surjective spectral isometries on certain non-simple unital C*-algebras are Jordan isomorphisms. Along the way, we establish several general facts in the setting of semisimple Banach algebras.Comment: 7 pages; paper available since July 201

Lie Isomorphisms of Nest Algebras

AbstractIn this paper we characterize linear mapsϕbetween two nest algebras T(N) and T(M) which satisfy the property thatϕ(AB−BA)=ϕ(A)ϕ(B)−ϕ(B)ϕ(A) for allA, B∈T(N). In particular, it is shown that such isomorphisms only exist if N is similar to M or M⊥

Characterizing Operations Preserving Separability Measures via Linear Preserver Problems

We use classical results from the theory of linear preserver problems to characterize operators that send the set of pure states with Schmidt rank no greater than k back into itself, extending known results characterizing operators that send separable pure states to separable pure states. We also provide a new proof of an analogous statement in the multipartite setting. We use these results to develop a bipartite version of a classical result about the structure of maps that preserve rank-1 operators and then characterize the isometries for two families of norms that have recently been studied in quantum information theory. We see in particular that for k at least 2 the operator norms induced by states with Schmidt rank k are invariant only under local unitaries, the swap operator and the transpose map. However, in the k = 1 case there is an additional isometry: the partial transpose map.Comment: 16 pages, typos corrected, references added, proof of Theorem 4.3 simplified and clarifie