Function algebras and flows. IV
HTML articles powered by AMS MathViewer
- by Paul S. Muhly
- Trans. Amer. Math. Soc. 203 (1975), 55-66
- DOI: https://doi.org/10.1090/S0002-9947-1975-0493358-9
- PDF | Request permission
Abstract:
The automorphisms of the algebra $\mathfrak {A}$ of analytic functions associated with a flow (without periodic orbits) are completely determined. This result extends earlier work of Arens who determined the automorphisms of $\mathfrak {A}$ when the flow is almost periodic. The Choquet boundary of the maximal ideal space of $\mathfrak {A}$ is also determined under the hypothesis that the flow has no fixed points.References
- Richard Arens, A Banach algebra generalization of conformal mappings of the disc, Trans. Amer. Math. Soc. 81 (1956), 501–513. MR 78658, DOI 10.1090/S0002-9947-1956-0078658-7
- Karel de Leeuw, Walter Rudin, and John Wermer, The isometries of some function spaces, Proc. Amer. Math. Soc. 11 (1960), 694–698. MR 121646, DOI 10.1090/S0002-9939-1960-0121646-9
- Robert Ellis, Lectures on topological dynamics, W. A. Benjamin, Inc., New York, 1969. MR 0267561
- Frank Forelli, Analytic and quasi-invariant measures, Acta Math. 118 (1967), 33–59. MR 209771, DOI 10.1007/BF02392475
- Frank Forelli, Conjugate functions and flows, Quart. J. Math. Oxford Ser. (2) 20 (1969), 215–233. MR 251462, DOI 10.1093/qmath/20.1.215
- Gerald M. Leibowitz, Lectures on complex function algebras, Scott, Foresman & Co., Glenview, Ill., 1970. MR 0428042
- Samuel Merrill, Maximality of certain algebras $H^{\infty }\,(dm)$, Math. Z. 106 (1968), 861–266. MR 234289, DOI 10.1007/BF01110274
- Paul S. Muhly, Function algebras and flows, Acta Sci. Math. (Szeged) 35 (1973), 111–121. MR 331068
- Paul S. Muhly, Function algebras and flows, Acta Sci. Math. (Szeged) 35 (1973), 111–121. MR 331068
- Paul S. Muhly, Function algebras and flows. III, Math. Z. 136 (1974), 253–260. MR 493357, DOI 10.1007/BF01214129
- Masao Nagasawa, Isomorphisms between commutative Banach algebras with an application to rings of analytic functions, K\B{o}dai Math. Sem. Rep. 11 (1959), 182–188. MR 121645
- Guido Weiss, Weak$^{\ast }$-Dirichlet algebras induced by the ergodic Hilbert transform, L’analyse harmonique dans le domaine complexe (Actes Table Ronde Internat., Centre Nat. Recherche Sci., Montpellier, 1972) Lecture Notes in Math., Vol. 336, Springer, Berlin, 1973, pp. 20–27. MR 0394216
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 203 (1975), 55-66
- MSC: Primary 46J10; Secondary 43A70
- DOI: https://doi.org/10.1090/S0002-9947-1975-0493358-9
- MathSciNet review: 0493358