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Injectivity and operator spaces. (English) Zbl 0341.46049


MSC:

46M10 Projective and injective objects in functional analysis
47L05 Linear spaces of operators
46L05 General theory of \(C^*\)-algebras
46L10 General theory of von Neumann algebras
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References:

[1] Alfsen, E. M., Compact Convex Sets and Boundary Integrals (1971), Springer-Verlag: Springer-Verlag Berlin · Zbl 0209.42601
[2] Arveson, W. B., Subalgebras of \(C^∗\)-algebras, II, Acta Math., 128, 271-308 (1972) · Zbl 0245.46098
[3] Bade, W. G., The Banach Space \(C(S)\), Aarhus University Lecture Notes Series No. 26 (1971) · Zbl 0224.46026
[4] Berberian, S. K.; Orland, G. H., On the closure of the numerical range of an operator, (Proc. Amer. Math. Soc., 18 (1967)), 499-503 · Zbl 0173.42104
[5] Bourbaki, N., Espaces Vectoriels Topologiques (1955), Hermann: Hermann Paris · Zbl 0066.35301
[6] Choi, M. D., Positive linear maps on \(C^∗\)-algebras, Canad. J. Math., 24, 520-529 (1972) · Zbl 0235.46090
[7] Choi, M. D., A Schwarz inequality for positive linear maps on \(C^∗\)-algebras, Illinois J. Math., 18, 565-574 (1974) · Zbl 0293.46043
[8] Choi, M. D., Completely positive linear maps on complex matrices, Linear Algebra and Appl., 10, 285-290 (1975) · Zbl 0327.15018
[9] Choquet, G., (Lectures on Analysis, Vol. II (1969), Benjamin: Benjamin New York)
[10] Connes, A., Une classification des facteurs de type III, Ann. Sci. École Norm. Sup., 6, 133-252 (1973) · Zbl 0274.46050
[11] Dixmier, J., Les algèbres d’opérateurs dans l’espace Hilbertien (1969), Gauthier-Villars: Gauthier-Villars Paris · Zbl 0175.43801
[12] Effros, E. G., Injective and tensor products for convex sets and \(C^∗\)-algebras, (Facial Structure of Compact Convex Sets and Applications (1972), NATO Advanced Study Institute: NATO Advanced Study Institute Swansea) · Zbl 0152.33203
[13] E. G. Effros and C. LanceAdvances in Math.; E. G. Effros and C. LanceAdvances in Math. · Zbl 0372.46064
[14] Hakeda, J.; Tomiyama, J., On some extension property of von Neumann algebras, Tôhoku Math. J., 19, 315-323 (1967) · Zbl 0175.14201
[15] Halmos, P. R., Finite-Dimensional Vector Spaces (1958), Van Nostrand: Van Nostrand Princeton, N.J · Zbl 0107.01404
[16] Halmos, P. R., (A Hilbert Space Problem Book (1967), Van Nostrand: Van Nostrand Princeton, N.J)
[17] Hirschfield, R. A.; Johnson, B. E., Spectral characterization of finite-dimensional algebras, Indag. Math., 34, 19-23 (1972) · Zbl 0232.46043
[18] Hustad, O., Intersection properties of balls in complex Banach spaces whose duals are \(L_1\) spaces, Acta Math., 132, 283-313 (1974) · Zbl 0309.46025
[19] Kadison, R. V., A representation theory for commutative topological algebra, Mem. Amer. Math. Soc., 7 (1951) · Zbl 0042.34801
[20] Kadison, R. V., A generalized Schwarz inequality and algebraic invariants for \(C^∗\)-algebras, Ann. of Math., 56, 494-503 (1952) · Zbl 0047.35703
[21] Kadison, R. V., Unitary invariants for representations of operator algebras, Ann. of Math., 66, 304-379 (1957) · Zbl 0084.10705
[22] Kaplansky, I., A theorem on rings of operators, Pacific J. Math., 1, 227-232 (1951) · Zbl 0043.11502
[23] Kelley, J. L.; Namioka, I., Linear Topological Spaces (1961), Van Nostrand: Van Nostrand Princeton, N.J, co-authors
[24] Lacey, E., The Isometric Theory of Classical Banach Spaces (1974), Springer-Verlag: Springer-Verlag Berlin · Zbl 0285.46024
[25] Lance, C., On nuclear \(C^∗\)-algebras, J. Functional Analysis, 12, 157-176 (1973) · Zbl 0252.46065
[26] Lance, C., Tensor products of nonunital \(C^∗\)-algebras, J. London Math. Soc., 12, 160-168 (1976), (2) · Zbl 0317.46050
[27] A. Lima; A. Lima · Zbl 0347.46017
[28] Loebl, R. I., Injective von Neumann algebras, (Proc. Amer. Math. Soc., 44 (1974)), 46-48 · Zbl 0283.46029
[29] Michael, E.; Pelczynski, A., Separable Banach spaces which admit \(C_{n^∞}\) approximations, Israel J. Math., 4, 189-198 (1966) · Zbl 0151.17602
[30] Pedersen, G., Operator algebras with weakly closed abelian subalgebras, Bull. London Math. Soc., 4, 171-175 (1972) · Zbl 0252.46071
[31] Pedersen, G.; Takesaki, M., The Radon-Nikodym theorem for von Neumann algebras, Acta Math., 130, 53-87 (1973) · Zbl 0262.46063
[32] Powers, R. T., Self-adjoint algebras of unbounded operators, II, Trans. Amer. Math. Soc., 187, 261-293 (1974) · Zbl 0296.46059
[33] Russo, B.; Dye, H. A., A note on unitary operators in \(C^∗\)-algebras, Duke Math. J., 33, 413-416 (1966) · Zbl 0171.11503
[34] Sakai, S., A characterization of \(W^∗\)-algebras, Pacific J. Math., 6, 763-773 (1956) · Zbl 0072.12404
[35] Sakai, S., On the Stone-Weierstrass theorem of \(C^∗\)-algebras, Tôhoku Math. J., 22, 191-199 (1970) · Zbl 0211.16001
[36] Schwartz, J., Two finite, hyperfinite, non-isomorphic factors, Comm. Pure Appl. Math., 16, 19-26 (1963) · Zbl 0131.33201
[37] Stinespring, W. F., Positive functions on \(C^∗\)-algebras, (Proc. Amer. Math. Soc., 6 (1955)), 211-216 · Zbl 0064.36703
[38] Størmer, E., Positive Linear Maps of \(C^∗\)-Algebras, (Lecture Notes in Physics, Vol. 29 (1974), Springer-Verlag: Springer-Verlag Berlin), 85-106
[39] Šmul’jan, Ju. L., An operator Hellinger integral, Mat. Sb., 91, 381-430 (1959), (Russian)
[40] Takesaki, M., On the conjugate space of operator algebra, Tôhoku Math. J., 10, 194-203 (1958) · Zbl 0089.10703
[41] Tomiyama, J., On the projection of norm one in \(W^∗\)-algebras, (Proc. Japan Acad., 33 (1957)), 608-612 · Zbl 0081.11201
[42] Tomiyama, J., Tensor products and projections of norm one in von Neumann algebras, (Lecture notes for seminar given at University of Copenhagen (1970)) · Zbl 0176.44002
[43] Connes, A., Classification of injective factors, Ann. of Math., 104, 73-116 (1976) · Zbl 0343.46042
[44] M. D. Choi and E. G. Effros\(C^∗\)Indiana Univ. Math. J.; M. D. Choi and E. G. Effros\(C^∗\)Indiana Univ. Math. J. · Zbl 0378.46052
[45] \( \textsc{S. Wasserman}C^∗\); \( \textsc{S. Wasserman}C^∗\)
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