Function algebras and flows. IV

Muhly, Paul S.

doi:10.1090/S0002-9947-1975-0493358-9

Function algebras and flows. IV
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by Paul S. Muhly PDF

Trans. Amer. Math. Soc. 203 (1975), 55-66 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