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Analytic functions of a proper contraction. (English) Zbl 0455.47013

MSC:
47A60 Functional calculus for linear operators
47A25 Spectral sets of linear operators
47A30 Norms (inequalities, more than one norm, etc.) of linear operators
30C99 Geometric function theory
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[1] Brickman, L., MacGregor, T.H., Wilken, D.R.: Convex hulls of some classical families of univalent functions. Trans. Amer. Math. Soc.156, 91-107 (1971) · Zbl 0227.30013 · doi:10.1090/S0002-9947-1971-0274734-2
[2] Dunford, N., Schwartz, J.T.: Linear operators, Part I: General theory. New York: Interscience 1958 · Zbl 0084.10402
[3] Gohberg, I.C., Krein, M.G.: Introduction to the theory of linear nonselfadjoint operators. Translations of Mathematical Monographs 18. Providence: Amer. Math. Soc. 1969 · Zbl 0181.13504
[4] Goluzin, G.M.: Geometric theory of functions of a complex variable. Translations of Mathematical Monographs 26. Providence: Amer. Math. Soc. 1969 · Zbl 0183.07502
[5] Halmos, P.R.: A Hilbert space problem book. Princeton: Van Nostrand 1967 · Zbl 0144.38704
[6] Harris, L.A.: Schwarz’s lemma in normed linear spaces. Proc. Nat. Acad. Sci. U.S.A.62, 1014-1017 (1969) · Zbl 0199.19401 · doi:10.1073/pnas.62.4.1014
[7] Heinz, E.: Ein v. Neumannscher Satz über beschränkte Operatoren im Hilbertschen Raum. Nachr. Akad. Wiss. Göttingen Math.-Phys. K1. II 5-6 (1952) · Zbl 0046.33702
[8] Hille, E.: Analytic function theory II. Boston: Ginn 1962 · Zbl 0102.29401
[9] Holland, F.: The extreme points of a class of functions with positive real part. Math. Ann.202, 85-87 (1973) · Zbl 0246.30027 · doi:10.1007/BF01351208
[10] Köthe, G.: Topological vector spaces I. Berlin-Heidelberg-New York: Springer 1969 · Zbl 0179.17001
[11] Nehari, Z.: Conformal mapping. New York: McGraw-Hill 1952 · Zbl 0048.31503
[12] Neumann, J. von: Eine Spektraltheorie für allgemeine Operatoren eines unitären Raumes. Math. Nachr.4, 258-281 (1950/51)
[13] Phillips, R.S.: On symplectic mappings of contraction operators. Studia Math.31, 15-27 (1968) · Zbl 0167.13501
[14] Pommerenke, C.: Univalent functions. Göttingen: Vandenhoeck-Ruprecht 1975
[15] Potapov, V.P.: The multiplicative structure of J-contractive matrix functions. Amer. Math. Soc. Transl. (2)15, 131-243 (1960) · Zbl 0090.05403
[16] Riesz, F., Sz.-Nagy, B.: Functional analysis. New York: Ungar 1960 · Zbl 0070.10902
[17] Rogosinski, W.: Über positive harmonische Entwicklungen und typisch-reelle Potenzreihen. Math. Z.35, 93-121 (1932) · Zbl 0003.39303 · doi:10.1007/BF01186552
[18] Schaefer, H.H.: Topological vector spaces. Berlin-Heidelberg-New York: Springer 1971 · Zbl 0212.14001
[19] Schober, G.: Univalent functions ? Selected topics. Berlin-Heidelberg-New York: Springer 1975 · Zbl 0306.30018
[20] Siegel, C.L.: Symplectic geometry. Amer. J. Math.65, 1-86 (1943) · Zbl 0138.31401 · doi:10.2307/2371774
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