94 research outputs found
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
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