Bhat, Rajarama; Pati, V.; Sunder, V. S. On some convex sets and their extreme points. (English) Zbl 0791.46006 Math. Ann. 296, No. 4, 637-648 (1993). ft is shown that the extreme points of the set of Markov maps of \(M(2,K)\), \(K=\mathbb{R}\) or \(\mathbb{C}\), are precisely the set of automorphisms, and that this statement is false for \(M(n,\mathbb{C})\), \(n\geq 4\) and \(M(n,\mathbb{R})\), \(n\geq 3\). We also show that if \(N\subset M\) is a pair of finite factors with Jones index \([M:N]= r^{-1}<\infty\), the extreme points of the set \(C(M,N)= \{x\in M_ +\): \(E_ N x=r\}\) are precisely the projections in \(C(M,N)\) if \(r={1\over 2}\), and in general, for \(r<{1\over 2}\), there may exist other extreme points of \(C(M,N)\). Reviewer: Rajarama Bhat (New Delhi) Cited in 1 ReviewCited in 5 Documents MSC: 46A55 Convex sets in topological linear spaces; Choquet theory 46L37 Subfactors and their classification Keywords:extreme points; set of Markov maps; automorphisms; factors; Jones index PDFBibTeX XMLCite \textit{R. Bhat} et al., Math. Ann. 296, No. 4, 637--648 (1993; Zbl 0791.46006) Full Text: DOI EuDML References: [1] Arveson, W.B.: Subalgebras ofC *-algebras. Acta Math.123, 141-224 (1969) · Zbl 0194.15701 · doi:10.1007/BF02392388 [2] Christensen, J.P.R., Vesterstrom, J.: A note on extreme positive definite matrices. Math. Ann.244, 65-68 (1979) · Zbl 0407.15018 · doi:10.1007/BF01420337 [3] Grone, R., Pierce, S., Watkins, W.: Extremal correlation matrices. Linear Algebra Appl.134, 63-70 (1990) · Zbl 0703.15028 · doi:10.1016/0024-3795(90)90006-X [4] Jones, V.F.R.: Index for subfactors. Invent. Math.72, 1-25 (1983) · Zbl 0508.46040 · doi:10.1007/BF01389127 [5] St?rmer, E.: Regular Abelian Banach algebras of linear maps of operators. J. Funct. Anal.37, 331-373 (1980) · Zbl 0458.46044 · doi:10.1016/0022-1236(80)90048-8 [6] Pimsner, M., Popa, S.: Entropy and index for subfactors. Ann. Sci. ?c. Norm. Sup?r., IV. Ser.19, 57-106 (1980) · Zbl 0646.46057 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.