Nica, Alexandru \(R\)-diagonal pairs arising as free off-diagonal compression. (English) Zbl 0879.46031 Indiana Univ. Math. J. 45, No. 2, 529-544 (1996). Summary: We show that if one takes a free off-diagonal compression of a *-free family of elements in a tracial \(C^*\)-probability space, then one obtains a free family of \(R\)-diagonal pairs, in the sense of A. Nica and P. Speicher [Fields Inst. Commun. 12, 149-188 (1997)]. The proof relies on the matrix version of the full Fock space model for the \(R\)-transform, recently introduced by D. Shlyakhtenko [C. R. Acad. Sci., Paris, Ser. I 332, No. 7, 645-649 (1996; Zbl 0847.46031)]. Cited in 2 Documents MSC: 46L51 Noncommutative measure and integration 46L53 Noncommutative probability and statistics 46L54 Free probability and free operator algebras 47A20 Dilations, extensions, compressions of linear operators Keywords:free off-diagonal compression; *-free family of elements; tracial \(C^*\)-probability space; \(R\)-diagonal pairs; Fock space model; \(R\)-transform Citations:Zbl 0847.46031 PDFBibTeX XMLCite \textit{A. Nica}, Indiana Univ. Math. J. 45, No. 2, 529--544 (1996; Zbl 0879.46031) Full Text: DOI