Takemoto, Hideo Approximate innerness of positive linear maps of finite von Neumann algebras. (English) Zbl 0579.46044 Proc. Am. Math. Soc. 94, 463-466 (1985). The completely positive linear maps give an important role in the theory of operator algebras. We have the famous Stinespring’s theorem for the completely positive linear maps and the Sakai’s theorem that the inner automorphism group is dense in the automorphism group for the hyperfinite \(II_ 1\)-factors. From the above mentioned two theorems, this report gives the connection between the completely positive linear maps and the approximate innerness for the finite von Neumann algebras. Cited in 1 ReviewCited in 1 Document MSC: 46L10 General theory of von Neumann algebras 46L30 States of selfadjoint operator algebras 46L40 Automorphisms of selfadjoint operator algebras Keywords:completely positive linear maps; Stinespring’s theorem; Sakai’s theorem; inner automorphism group; approximate innerness for the finite von Neumann algebras PDFBibTeX XMLCite \textit{H. Takemoto}, Proc. Am. Math. Soc. 94, 463--466 (1985; Zbl 0579.46044) Full Text: DOI References: [1] Man Duen Choi, A Schwarz inequality for positive linear maps on \?*-algebras, Illinois J. Math. 18 (1974), 565 – 574. · Zbl 0293.46043 [2] Uffe Haagerup, The standard form of von Neumann algebras, Math. Scand. 37 (1975), no. 2, 271 – 283. · Zbl 0304.46044 · doi:10.7146/math.scand.a-11606 [3] -, A new proof of the equivalence of injectivity and hyperfiniteness for factors on a separable Hilbert space (preprint). · Zbl 0586.46047 [4] Shôichirô Sakai, On automorphism groups of \?\?\(_{1}\)-factors, Tôhoku Math. J. (2) 26 (1974), 423 – 430. · Zbl 0303.46060 · doi:10.2748/tmj/1178241136 [5] W. Forrest Stinespring, Positive functions on \?*-algebras, Proc. Amer. Math. Soc. 6 (1955), 211 – 216. · Zbl 0064.36703 [6] Masamichi Takesaki, Theory of operator algebras. I, Springer-Verlag, New York-Heidelberg, 1979. · Zbl 0436.46043 [7] J. Tomiyama, Complete positivity in operator algebras, Lecture Note No. 4, RIMS, Kyoto Univ., 1978. (Japanese) 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.