Function algebras
HTML articles powered by AMS MathViewer
- by H. L. Royden PDF
- Bull. Amer. Math. Soc. 69 (1963), 281-298
References
- Richard Arens, The maximal ideals of certain functions algebras, Pacific J. Math. 8 (1958), 641–648. MR 117537, DOI 10.2140/pjm.1958.8.641
- Richard Arens and A. P. Calderón, Analytic functions of several Banach algebra elements, Ann. of Math. (2) 62 (1955), 204–216. MR 71735, DOI 10.2307/1969675
- Richard Arens and I. M. Singer, Function values as boundary integrals, Proc. Amer. Math. Soc. 5 (1954), 735–745. MR 65024, DOI 10.1090/S0002-9939-1954-0065024-7
- Richard Arens and I. M. Singer, Generalized analytic functions, Trans. Amer. Math. Soc. 81 (1956), 379–393. MR 78657, DOI 10.1090/S0002-9947-1956-0078657-5
- H. S. Bear, Complex function algebras, Trans. Amer. Math. Soc. 90 (1959), 383–393. MR 107164, DOI 10.1090/S0002-9947-1959-0107164-9
- H. S. Bear, A strong maximum modulus theorem for maximal function algebras, Trans. Amer. Math. Soc. 92 (1959), 464–469. MR 115106, DOI 10.1090/S0002-9947-1959-0115106-5
- H. S. Bear, Some boundary properties of function algebras, Proc. Amer. Math. Soc. 11 (1960), 1–4. MR 113152, DOI 10.1090/S0002-9939-1960-0113152-2
- Lipman Bers, On rings of analytic functions, Bull. Amer. Math. Soc. 54 (1948), 311–315. MR 24970, DOI 10.1090/S0002-9904-1948-08992-3
- Errett Bishop, The structure of certain measures, Duke Math. J. 25 (1958), 283–289. MR 99441
- Errett Bishop, Subalgebras of functions on a Riemann surface, Pacific J. Math. 8 (1958), 29–50. MR 96818, DOI 10.2140/pjm.1958.8.29
- Errett Bishop, Approximation by a polynomial and its derivatives on certain closed sets, Proc. Amer. Math. Soc. 9 (1958), 946–953. MR 109225, DOI 10.1090/S0002-9939-1958-0109225-1
- Errett Bishop, Some theorems concerning function algebras, Bull. Amer. Math. Soc. 65 (1959), 77–78. MR 109304, DOI 10.1090/S0002-9904-1959-10283-4
- Errett Bishop, Boundary measures of analytic differentials, Duke Math. J. 27 (1960), 331–340. MR 118852
- Errett Bishop, A generalization of the Stone-Weierstrass theorem, Pacific J. Math. 11 (1961), 777–783. MR 133676, DOI 10.2140/pjm.1961.11.777
- Errett Bishop, A general Rudin-Carleson theorem, Proc. Amer. Math. Soc. 13 (1962), 140–143. MR 133462, DOI 10.1090/S0002-9939-1962-0133462-4
- Errett Bishop, Analyticity in certain Banach algebras, Trans. Amer. Math. Soc. 102 (1962), 507–544. MR 142015, DOI 10.1090/S0002-9947-1962-0142015-8
- Errett Bishop and Karel de Leeuw, The representations of linear functionals by measures on sets of extreme points, Ann. Inst. Fourier (Grenoble) 9 (1959), 305–331. MR 114118, DOI 10.5802/aif.95
- N. Bruschlinsky, Stetige Abbildungen und Bettische Gruppen der Dimensionszahlen 1 und 3, Math. Ann. 109 (1934), no. 1, 525–537 (German). MR 1512908, DOI 10.1007/BF01449153 19. H. Cartan, Faisceaux analytiques sur les variétés de Stein, Exposé XVIII, Séminare de Cartan, 1951-52, Theorie des fonctions de plusieurs variables.
- Paul Civin, A maximum modulus property of maximal subalgebras, Proc. Amer. Math. Soc. 10 (1959), 51–54. MR 105032, DOI 10.1090/S0002-9939-1959-0105032-5
- Paul Civin and Bertram Yood, Regular Banach algebras with a countable space of maximal regular ideals, Proc. Amer. Math. Soc. 7 (1956), 1005–1010. MR 82649, DOI 10.1090/S0002-9939-1956-0082649-5
- R. E. Edwards, Algebras of holomorphic functions, Proc. London Math. Soc. (3) 7 (1957), 510–517. MR 92998, DOI 10.1112/plms/s3-7.1.510 23. S. Eilenberg, Transformations continues en circonférence et la topologie du plan, Fund. Math. 26 (1936), 61-112.
- Samuel Eilenberg and Norman Steenrod, Foundations of algebraic topology, Princeton University Press, Princeton, N.J., 1952. MR 0050886, DOI 10.1515/9781400877492
- I. Gelfand, Normierte Ringe, Rec. Math. [Mat. Sbornik] N. S. 9 (51) (1941), 3–24 (German, with Russian summary). MR 0004726
- I. M. Gel′fand, D. A. Raĭkov, and G. E. Šilov, Commutative normed rings, Uspehi Matem. Nauk (N. S.) 1 (1946), no. 2(12), 48–146 (Russian). MR 0027130 27. L. Gilman, and M. Jerison, Rings of continuous functions, Van Nostrand, Princeton, N. J., 1959. 28. A. M. Gleason, Function algebras, Seminars on analytic functions, Institute for Advance Study, Princeton, N. J., 1957.
- Maurice Heins, Algebraic structure and conformal mapping, Trans. Amer. Math. Soc. 89 (1958), 267–276. MR 96786, DOI 10.1090/S0002-9947-1958-0096786-9
- Olaf Helmer, Divisibility properties of integral functions, Duke Math. J. 6 (1940), 345–356. MR 1851
- Henry Helson and Frank Quigley, Existence of maximal ideals in algebras of continuous functions, Proc. Amer. Math. Soc. 8 (1957), 115–119. MR 84731, DOI 10.1090/S0002-9939-1957-0084731-6
- Henry Helson and Frank Quigley, Maximal algebras of continuous functions, Proc. Amer. Math. Soc. 8 (1957), 111–114. MR 84732, DOI 10.1090/S0002-9939-1957-0084732-8
- Melvin Henriksen, On the ideal structure of the ring of entire functions, Pacific J. Math. 2 (1952), 179–184. MR 47928, DOI 10.2140/pjm.1952.2.179
- Edwin Hewitt, Rings of real-valued continuous functions. I, Trans. Amer. Math. Soc. 64 (1948), 45–99. MR 26239, DOI 10.1090/S0002-9947-1948-0026239-9
- F. Hirzebruch, Neue topologische Methoden in der algebraischen Geometrie, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Heft 9, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1956 (German). MR 0082174
- Kenneth Hoffman, Boundary behavior of generalized analytic functions, Trans. Amer. Math. Soc. 87 (1958), 447–466. MR 96942, DOI 10.1090/S0002-9947-1958-0096942-X
- Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0133008 38. K. Hoffman, Log modular algebras, (to appear).
- Kenneth Hoffman and I. M. Singer, Maximal subalgebras of $C(\Gamma )$, Amer. J. Math. 79 (1957), 295–305. MR 85478, DOI 10.2307/2372683
- K. Goffman and I. M. Zinger, Some problems of Gel′fand, Uspehi Mat. Nauk 14 (1959), no. 3 (87), 99–114 (Russian). MR 0117538
- K. Hoffman and I. M. Singer, Maximal algebras of continuous functions, Acta Math. 103 (1960), 217–241. MR 117540, DOI 10.1007/BF02546357
- Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, vol. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
- Shizuo Kakutani, Rings of analytic functions, Lectures on functions of a complex variable, University of Michigan Press, Ann Arbor, Mich., 1955, pp. 71–83. MR 0070060 44. S. Kakutani, On rings of bounded analytic functions, Seminars on analytic functions, Vol. 2, Institute for Advanced Study, Princeton, N. J., 1957, pp. 298-311.
- Henry J. Landau, On uniform approximation to continuous functions by rational functions with preassigned poles, Proc. Amer. Math. Soc. 5 (1954), 671–676. MR 64140, DOI 10.1090/S0002-9939-1954-0064140-3
- K. deLeeuw, A type of convexity in the space of $n$-complex variables, Trans. Amer. Math. Soc. 83 (1956), 193–204. MR 80751, DOI 10.1090/S0002-9947-1956-0080751-X
- K. de Leeuw, Functions on circular subsets of the space of $n$ complex variables, Duke Math. J. 24 (1957), 415–431. MR 94723, DOI 10.1215/S0012-7094-57-02449-3
- Z. L. Leĭbenzon, On the ring of continuous functions on a circle, Uspehi Matem. Nauk (N.S.) 7 (1952), no. 4(50), 163–164 (Russian). MR 0050809
- Hans Lewy, On the local character of the solutions of an atypical linear differential equation in three variables and a related theorem for regular functions of two complex variables, Ann. of Math. (2) 64 (1956), 514–522. MR 81952, DOI 10.2307/1969599
- Lynn H. Loomis, An introduction to abstract harmonic analysis, D. Van Nostrand Co., Inc., Toronto-New York-London, 1953. MR 0054173
- S. N. Mergelyan, Uniform approximations of functions of a complex variable, Uspehi Matem. Nauk (N.S.) 7 (1952), no. 2(48), 31–122 (Russian). MR 0051921
- Hugo Rossi, The local maximum modulus principle, Ann. of Math. (2) 72 (1960), 1–11. MR 117539, DOI 10.2307/1970145
- Hugo Rossi, Algebras of holomorphic functions on one-dimensional varieties, Trans. Amer. Math. Soc. 100 (1961), 439–458. MR 131164, DOI 10.1090/S0002-9947-1961-0131164-5
- H. L. Royden, Rings of analytic and meromorphic functions, Trans. Amer. Math. Soc. 83 (1956), 269–276. MR 89908, DOI 10.1090/S0002-9947-1956-0089908-5
- H. L. Royden, Rings of meromorphic functions, Proc. Amer. Math. Soc. 9 (1958), 959–965. MR 103974, DOI 10.1090/S0002-9939-1958-0103974-7
- Walter Rudin, Analyticity, and the maximum modulus principle, Duke Math. J. 20 (1953), 449–457. MR 56076
- Walter Rudin, Some theorems on bounded analytic functions, Trans. Amer. Math. Soc. 78 (1955), 333–342. MR 67192, DOI 10.1090/S0002-9947-1955-0067192-5
- Walter Rudin, Multiplicative groups of analytic functions, Proc. Amer. Math. Soc. 6 (1955), 83–87. MR 66449, DOI 10.1090/S0002-9939-1955-0066449-7
- Walter Rudin, Boundary values of continuous analytic functions, Proc. Amer. Math. Soc. 7 (1956), 808–811. MR 81948, DOI 10.1090/S0002-9939-1956-0081948-0
- Walter Rudin, Subalgebras of spaces of continuous functions, Proc. Amer. Math. Soc. 7 (1956), 825–830. MR 82650, DOI 10.1090/S0002-9939-1956-0082650-1
- Walter Rudin, Continuous functions on compact spaces without perfect subsets, Proc. Amer. Math. Soc. 8 (1957), 39–42. MR 85475, DOI 10.1090/S0002-9939-1957-0085475-7
- Walter Rudin, The closed ideals in an algebra of analytic functions, Canadian J. Math. 9 (1957), 426–434. MR 89254, DOI 10.4153/CJM-1957-050-0
- I. J. Schark, Maximal ideals in an algebra of bounded analytic functions, J. Math. Mech. 10 (1961), 735–746. “I. J. Schark” is a pseudonym for the group: Irving Kaplansky, John Wermer, Shizuo Kakutani, R. Creighton Buck, Halsey Royden, Andrew Gleason, Richard Arens and Kenneth Hoffman. MR 0125442
- G. E. Šilov, On rings of functions with uniform convergence, Ukrain. Mat. Žurnal 3 (1951), 404–411 (Russian). MR 0054178
- G. E. Šilov, On the decomposition of a commutative normed ring into a direct sum of ideals, Amer. Math. Soc. Transl. (2) 1 (1955), 37–48. MR 0073946, DOI 10.1090/trans2/001/03
- Gabriel Stolzenberg, Polynomially convex sets, Bull. Amer. Math. Soc. 68 (1962), 382–387. MR 151642, DOI 10.1090/S0002-9904-1962-10816-7
- Gabriel Stolzenberg, A hull with no analytic structure, J. Math. Mech. 12 (1963), 103–111. MR 0143061
- John Wermer, On algebras of continuous functions, Proc. Amer. Math. Soc. 4 (1953), 866–869. MR 58877, DOI 10.1090/S0002-9939-1953-0058877-9
- John Wermer, Algebras with two generators, Amer. J. Math. 76 (1954), 853–859. MR 64321, DOI 10.2307/2372659
- John Wermer, Subalgebras of the algebra of all complex-valued continuous functions on the circle, Amer. J. Math. 78 (1956), 225–242. MR 84729, DOI 10.2307/2372513
- John Wermer, Rings of analytic functions, Ann. of Math. (2) 67 (1958), 497–516. MR 96817, DOI 10.2307/1969870
- John Wermer, The hull of a curve in $C^{n}$, Ann. of Math. (2) 68 (1958), 550–561. MR 100102, DOI 10.2307/1970155
- John Wermer, Rings of analytic functions, Ann. of Math. (2) 67 (1958), 497–516. MR 96817, DOI 10.2307/1969870
- John Wermer, The maximum principle for bounded functions, Ann. of Math. (2) 69 (1959), 598–604. MR 109885, DOI 10.2307/1970025
- John Wermer, Dirichlet algebras, Duke Math. J. 27 (1960), 373–381. MR 121671
- John Wermer, Banach algebras and analytic functions, Advances in Math. 1 (1961), no. fasc. 1, 51–102. MR 143063, DOI 10.1016/0001-8708(65)90036-8
Additional Information
- Journal: Bull. Amer. Math. Soc. 69 (1963), 281-298
- DOI: https://doi.org/10.1090/S0002-9904-1963-10900-3
- MathSciNet review: 0149327