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Linear Preserver Problems
"... ... in this article. In the first three sections, we discuss motivation, results, and problems. In the last three sections, we describe some techniques, outline a few proofs, and discuss some exceptional results. ..."
Abstract

Cited by 30 (9 self)
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... in this article. In the first three sections, we discuss motivation, results, and problems. In the last three sections, we describe some techniques, outline a few proofs, and discuss some exceptional results.
On Almost Linearity
 of Low Dimensional Projections From High Dimensional Data, The Annals of Statistics
, 1993
"... maps transforming the higher numerical ranges ..."
Linear Preserver Problems
"... this article. In the first three sections, we discuss motivation, results, and problems. In the last three sections, we describe some techniques, outline a few proofs, and discuss some exceptional results ..."
Abstract
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this article. In the first three sections, we discuss motivation, results, and problems. In the last three sections, we describe some techniques, outline a few proofs, and discuss some exceptional results
Preserving zeros of a polynomial ∗
, 706
"... We study nonlinear surjective mappings on subsets of Mn(F), which preserve the zeros of some fixed polynomials in noncommuting variables. ..."
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We study nonlinear surjective mappings on subsets of Mn(F), which preserve the zeros of some fixed polynomials in noncommuting variables.
MAPS ON POSITIVE OPERATORS PRESERVING LEBESGUE DECOMPOSITIONS ∗
"... Abstract. Let H be a complex Hilbert space. Denote by B(H) + the set of all positive bounded linear operators on H. A bijectiv e map φ: B(H) + → B(H) + is said to preserve Lebesgue decompositions in both directions if for any quadruple A, B, C, D of positive operators, B = C + D is an ALebesgue dec ..."
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Abstract. Let H be a complex Hilbert space. Denote by B(H) + the set of all positive bounded linear operators on H. A bijectiv e map φ: B(H) + → B(H) + is said to preserve Lebesgue decompositions in both directions if for any quadruple A, B, C, D of positive operators, B = C + D is an ALebesgue decomposition of B if and only if φ(B) =φ(C)+φ(D) isaφ(A)Lebesgue decomposition of φ(B). It is proved that every such transformation φ is of the form φ(A) =SAS ∗ (A ∈ B(H) +) for some invertible bounded linear or conjugatelinear operator S on H.
Preservers of Maximally Entangled States
, 2013
"... The linear structure of the real space spanned by maximally entangled states is investigated, and used to completely characterize those linear maps preserving the set of maximally entangled states on Mm ⊗ Mm, where Mm denotes the space of m × m complex matrices. Aside from a degenerate rank one map, ..."
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The linear structure of the real space spanned by maximally entangled states is investigated, and used to completely characterize those linear maps preserving the set of maximally entangled states on Mm ⊗ Mm, where Mm denotes the space of m × m complex matrices. Aside from a degenerate rank one map, such preservers are generated by a change of orthonormal basis in each tensor factor, interchanging the two tensor factors, and the transpose operator.