References
Arveson, W. B., On subalgebras ofC *-algebras.Bull. Amer. Math. Soc., 75 (1969), 790–794.
Brown, A. &Halmos, P. R., Algebraic properties of Toeplitz operators.J. Reine Angew. Math., 213 (1963), 89–102.
Coburn, L. A., TheC *-algebra generated by an isometry.Bull. Amer. Math. Soc., 73 (1967), 722–726.
Dixmier, J.,Les C *-algèbres et leurs representations. Gauthier-Villars, Paris, 1964.
—,Les algèbres d'operateurs dans l'espace Hilbertien. Gauthier-Villars, Paris, 1957.
Dunford, N. &Schwartz, J. T.,Linear operators, part I. Interscience, New York, 1958.
Glimm, J., On a certain class of operator algebras.Trans. Amer. Math. Soc., 95 (1960), 318–340.
—, A Stone-Weierstrass theorem forC *-algebras.Ann. of Math., 72 (1960), 216–244.
Halmos, P. R.,A Hilbert space problem book, Van Nostrand., Princeton, 1967.
Helson, H.,Lectures on invariant subspaces. Academic Press, New York, 1964.
Hoffman, K.,Banach spaces of analytic functions. Prentice-Hall, Englewood Cliffs, 1962.
Ionescu-Tulcea, A. &Ionescu-Tulcea C., On the lifting property (1).J. Math. Anal. Appl., 3 (1961), 537–546.
Kadison, R. V., A generalized Schwarz inequality and algebraic invariants for operator algebras.Ann. of Math., 56 (1952), 494–503.
—, THe trace in finite operator algebras.Proc. Amer. Math. Soc., 12 (1961), 973–977.
Kelley, J., Namioka, I., and co-authors,Linear topological spaces. Van Nostrand, Princeton, 1963.
Phelps, R. R.,Lectures on Choquet's theorem. Van Nostrand, Princeton, 1966.
Rickart, C. E.,Banach algebras. Van Nostrand. Princeton, 1960.
Riesz, F. &Sz.-Nagy, B.,Functional analysis. Frederick Ungar, New York, 1955.
Rudin, W., Boundary values of continuous analytic functions.Proc. Amer. Math. Soc., 7 (1956), 808–811.
Sarason, D. E., On spectral sets having connected complement.Acta Sci. Math. (Szeged), 26 (1956), 289–299.
—, A note on the Volterra operator.J. Math. Anal. Appl., 12 (1965), 244–246.
—, Generalized interpolation inH ∞.Trans. Amer. Math. Soc., 127 (1967), 179–203.
Stinespring, W. F., Positive functions onC *-algebras.Proc. Amer. Math Soc., 6 (1955), 211–216.
Størmer, E., Positive linear maps of operator algebras.Acta Math., 110 (1963), 233–278.
Sz.-Nagy, B.,Extensions of linear transformations in Hilbert space, which extend beyond this space. Appendix to [18].
Sz.-Nagy, B., &Foias, C., Sur les contractions de l'espace de Hilbert VIII.Acta Sci. Math. (Szeged), 25 (1964), 38–71.
Takesaki, M., A note on the cross-norm of the direct product of operator algebra.Kodai Math. Seminar Reports, 10 (1958), 137–140.
Topping, D., UHF algebras are singly generated.Math. Scand., 22 (1968), 224–226.
Rosenberg, A., The number of irreducible representations of simple rings with no minimal ideals.Amer. J. Math. 75 (1953), 523–530.
Arveson, W. B., Unitary invariants for compact operators.Bull. Amer. Math. Soc., 76 (1970) (to appear).
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Research supported by NSF grant GP-5585 and the U.S. Army Research Office, Durham.
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Arveson, W.B. Subalgebras ofC *-algebras. Acta Math. 123, 141–224 (1969). https://doi.org/10.1007/BF02392388
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DOI: https://doi.org/10.1007/BF02392388