On the geometry of positive maps in matrix algebras. II
نویسندگان
چکیده
منابع مشابه
A Class of Linear Positive Maps in Matrix Algebras II
A class of linear positive, trace preserving maps in Mn is given in terms of affine maps in R n 2 −1 which map the closed unit ball into itself.
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We will be concerned with linear positive maps φ : Mm(C) → Mn(C). To fix notation we begin with setting up the notation and the relevant terminology (cf. [7]). We say that φ is positive if φ(A) is a positive element in Mn(C) for every positive matrix from Mm(C). If k ∈ N, then φ is said to be k-positive (respectively k-copositive) whenever [φ(Aij)] k i,j=1 (respectively [φ(Aji)] k i,j=1) is pos...
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نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.
15 صفحه اولMultiplicativity properties of entrywise positive maps on matrix algebras
Multiplicativity of certain maximal p → q norms of a tensor product of linear maps on matrix algebras is proved in situations in which the condition of complete positivity (CP) is either augmented by, or replaced by, the requirement that the entries of a matrix representative of the map are non-negative (EP). In particular, for integer t, multiplicativity holds for the maximal 2 → 2t norm of a ...
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As usually, a density matrix of M, is understood to be a non-negative matrix with trace equal to one. Thus, stochastic mappings are exactly those linear maps on M, which carry density matrices into density matrices. In this paper we shall deal with a particular case of the following problem concerning density matrices and stochastic transformations: Give necessary and sufficient conditions unde...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1985
ISSN: 0024-3795
DOI: 10.1016/0024-3795(85)90074-6