Størmer, Erling A decomposition theorem for positive maps, and the projection onto a spin factor. (English) Zbl 1345.46059 Math. Scand. 118, No. 1, 106-118 (2016). The paper is devoted to the structure of positive maps between \( C^\ast\)-algebras in the finite-dimensional case. The author shows that each positive map between matrix algebras is the sum of a maximal decomposable map and an atomic map which is both optimal and co-optimal (so-called bi-optimal), i.e., it majorizes neither a non-zero completely positive map nor a co-positive map. In order to obtain a deeper understanding of this decomposition he considers it in detail for the trace invariant positive projection of the full matrix algebra \(M_{2^n}\) onto a spin factor inside it. Explicit formulas are obtained for the decomposable map and the bi-optimal map in the decomposition when the spin factor is irreducible and contained in the \(2^n\) by \(2^n\) matrices over the quaternions. Reviewer: Sh. A. Ayupov (Tashkent) Cited in 1 Document MSC: 46L57 Derivations, dissipations and positive semigroups in \(C^*\)-algebras 47B65 Positive linear operators and order-bounded operators 46L05 General theory of \(C^*\)-algebras 46L70 Nonassociative selfadjoint operator algebras Keywords:\( C^\ast\)-algebra; spin factor; positive maps; completely positive map; decomposable map; atomic map; bi-optimal map PDFBibTeX XMLCite \textit{E. Størmer}, Math. Scand. 118, No. 1, 106--118 (2016; Zbl 1345.46059) Full Text: DOI arXiv