References
[A1] Agler, J.: An invariant subspace theorem. J. Funct. Anal.38, 315–323 (1980)
[A2] Agler, J.: Rational dilation on an annulus. Ann. Math.121, 537–563 (1985)
[A3] Agler, J.: Some interpolation theorems of Nevanlinna-Pick type. Preprint
[And] Ando, T.: On a pair of commutative contractions. Acta Sci. Math.24, 88–90 (1963)
[Arv 1] Arveson, W.B.: Subalgebras ofC *-algebras. Acta Math.123, 141–224 (1969)
[Arv 2] Arveson, W.B.: Subalgebras ofC *-algebras II. Acta Math.128, 271–308 (1972)
[B] Berger, C.: Normal dilations. Doctoral dissertation, Cornell University, 1968
[C1] Carathéodory, C.: Über das Schwarzsche Lemma bei analytischen Funktionen von zwei komplexen Veränderlichen. Math. Ann.97, 76–98 (1926)
[C2] Carathéodory, C.: Über die Geometrie der analytischen Abbildungen, die durch analytischen Funktionen von zwei Veränderlichen vermittelt werden. Abh. Math. Sem. Univ. Hamb.6, 97–145 (1928)
[Con] Conway, J.B.: A course in functional analysis. New York: Springer 1985
[Cur] Curto, R.: Applications of several complex variables to multiparameter spectral theory. Surveys of some recent results in operator theory, vol. II. Essex: Longman 1988
[D] Douglas, R., Paulsen, V.: Hilbert modules over function algebras. Essex: Longman 1989
[F] Fillmore, P.A.: Notes on operator theory. New York: Van Nostrand Reinhold 1970
[Foi] Foias, C.: Certaines applications des ensembles spectraux. 1. Mesure harmoniquespectrale. Stud. Cercet. Mat10, 365–401 (1959)
[K] Kobayashi, S.: Holomorphic manifolds and holomorphic mappings. New York: Marcel Dekker 1970
[Kr] Krantz, S.G.: Function Theory of Several Complex Variables. New York: John Wiley and Sons 1982
[Lau] Lautzenheiser, R.: Spectral sets, reducing subspaces, and function algebras. Thesis, Indiana University, 1973
[Leb] Lebow, A.: On von Neumann's theory of spectral sets. J. Math. Anal. Appl.7, 64–90 (1963)
[L1] Lempert, L.: La metrique de Kobayashi et la representation des domaines sur la boule. Bull. Soc. Math. France109, 427–474 (1981)
[L2] Lempert, L.: Intrinsic metrics. Proc. Symp. Pure Math.41, 147–150 (1984)
[Mis] Misra, G.: Curvature inequalities and extremal properties of bundle shifts. Preprint
[M] Mlak, W.: Partitions of spectral sets. Ann. Pol. Math.25, 273–280 (1972)
[Par] Parrott, S.: Unitary dilations for commuting contractions. Pac. J. Math.34, 481–490 (1970)
[P1] Paulsen, V.: Toward a theory ofK-spectral sets. Surveys of some recent results in operator theory, vol. II. Essex: Longman 1988
[P2] Paulsen, V.: K-spectral values for some finite matrices. J. Oper. Theory18, 249–264 (1987)
[R, W] Royden, H., Wong, P.: Caratheodory and Kobayashi metric on convex domains. Preprint
[S] Sarason, D.: On spectral sets having connected complement. Acta Sci. Math.26, 289–299 (1965)
[Sz.-N] Sz.-Nagy, B.: Sur les contractions de l'espace de Hilbert. Acta Sci. Math.15, 87–92 (1953)
[Sz.-N, F] Sz.-Nagy, B., Foias, C.: Harmonic analysis of operators on Hilbert space. Amsterdam-London: North Holland 1970
[T1] Taylor, J.L.: A joint spectrum for several commuting operators. J. Funct. Anal.6, 172–191 (1970)
[T2] Taylor, J.L.: An analytic-functional calculus for several commuting operators. Acta Math.125, 1–38 (1970)
[V] Varopoulos, N.: On an inequality of von Neumann and an application of the metric theory of tensor products to operator theory. J. Funct. Anal.16, 83–100 (1974)
[vN] von Neumann, J.: Eine Spektraltheorie für allgemeine Operatoren eines unitären Raumes. Math. Nachr.4, 258–281 (1951)
[W] Wermer, J.: Banach algebras and several complex variables. New York: Springer 1976
Author information
Authors and Affiliations
Additional information
Oblatum 19-IX-1988 & 6-XI-1989
Rights and permissions
About this article
Cite this article
Agler, J. Operator theory and the Carathéodory metric. Invent Math 101, 483–500 (1990). https://doi.org/10.1007/BF01231512
Issue Date:
DOI: https://doi.org/10.1007/BF01231512