References
Alaoglu, L., Weak topologies of normed linear spaces.Ann. of Math., 41 (1940), 252–267.
Bonsall, F. F., Extreme maximal ideals of partially ordered vector spaces,Proc. Amer. Math. Soc., (1956), 831–837.
Dixmier, J.,Les algèbres d'opérateurs dans l'espace hilbertien,. Paris, Gauthier-Villars, 1957.
Gelfand, I. &Neumark, M., On the imbedding of normed rings into the rings of operators in Hilbert space.Rec. Math. (Mat. Sbornik) N.S., 12 (1943), 197–213.
Glimm, J., A Stone-Weierstrass theorem forC *-algebras.Ann. of Math., 72 (1960), 216–244.
—, Type IC *-algebras,Ann. of Math., 73 (1961), 572–612.
Glimm, J. &Kadison, R. V., Unitary operators inC *-algebras.Pacific J. of Math., 10 (1960), 547–556.
Ionescu-Tulcea, A. &C., On the lifting property (1).J. of Math. Anal. and Applications, 3 (1961), 537–546.
Kadison, R. V., A representation theory for commutative topological algebra.Mem. Amer. Math. Soc., no. 7 (1951).
—, Isometries of operator algebras.Ann. of Math., 54 (1951), 325–338.
—, A generalized Schwarz inequality and algebraic invariants for operator algebras,Ann. of Math., 56 (1952), 494–503.
—, Irreducible operator algebras.Proc. Nat. Acad. Sci. U.S.A., 43 (1957), 273–276.
—, Unitary invariants for representations of operator algebras.Ann. of Math., 66 (1957), 304–379.
—, The trace in finite operator algebras.Proc. Amer. Math. Soc., 12 (1961), 973–977.
Kadison, R. V. &Singer, I. M., Extensions of pure states.Amer. J. Math., 81 (1959), 384–400.
Kaplansky, I., The structure of certain operator algebras.Trans. Amer. Math. Soc., 70 (1951), 219–255.
Krein, M. &Milman, O., On the extreme points of regular convex sets.Studia Math., 9 (1940), 133–137.
Segal, I. E., Irreducible representations of operator algebras.Bull. Amer. Math. Soc., 53 (1947), 73–88.
—, Two-sided ideals in operator algebras.Ann. of Math., 50 (1949), 856–865.
Stinespring, W. F., Positive functions onC *-algebras.Proc. Amer. Math. Soc., 6 (1955), 211–216.
Turumaru, T., On the direct-product of operator algebras I.Tôhoku Math. J. Second series, 4 (1952), 242–257.
Author information
Authors and Affiliations
Additional information
This work has been partially supported by the National Science Foundation under Grant no. 19022.
Rights and permissions
About this article
Cite this article
Størmer, E. Positive linear maps of operator algebras. Acta Math. 110, 233–278 (1963). https://doi.org/10.1007/BF02391860
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02391860