×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Alfsen, E.M., Compact convex sets and boundary integrals, (1971), Springer-Verlag Berlin · Zbl 0209.42601
[2] Arveson, W.B.; Arveson, W.B., Subalgebras of C∗-algebras, II, Acta math., 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, (), 499-503 · Zbl 0173.42104
[5] Bourbaki, N., Espaces vectoriels topologiques, (1955), 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., ()
[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 Paris · Zbl 0175.43801
[12] Effros, E.G., Injective and tensor products for convex sets and C∗-algebras, () · Zbl 0152.33203
[13] \scE. G. Effros and C. Lance, Tensor products of operator algebras, Advances in Math., to appear. · 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 Princeton, N.J · Zbl 0107.01404
[16] Halmos, P.R., ()
[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 L1 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 Princeton, N.J, co-authors
[24] Lacey, E., The isometric theory of classical Banach spaces, (1974), 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] \scA. Lima, Intersection properties of balls and subspaces in Banach spaces, to appear. · Zbl 0347.46017
[28] Loebl, R.I., Injective von Neumann algebras, (), 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, (), 211-216 · Zbl 0064.36703
[38] Størmer, E., Positive linear maps of C∗-algebras, (), 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, (), 608-612 · Zbl 0081.11201
[42] Tomiyama, J., Tensor products and projections of norm one in von Neumann algebras, () · Zbl 0176.44002
[43] Connes, A., Classification of injective factors, Ann. of math., 104, 73-116, (1976) · Zbl 0343.46042
[44] \scM. D. Choi and E. G. Effros, Nuclear C∗-algebras and injectivity: the general case, Indiana Univ. Math. J., to appear. · Zbl 0378.46052
[45] \scS. Wasserman, On tensor products of certain group C∗-algebras, to appear.
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.