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The structure of ideals and point derivations in Banach algebras of Lipschitz functions. (English) Zbl 0121.10204

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[1] Richard F. Arens and James Eells Jr., On embedding uniform and topological spaces, Pacific J. Math. 6 (1956), 397 – 403. · Zbl 0073.39601
[2] Edward James McShane and Truman Arthur Botts, Real analysis, The University Series in Undergraduate Mathematics, D. Van Nostrand Company, Inc., Princeton, N.J.-Toronto-London-New York, 1959. · Zbl 0087.04602
[3] R. Buck, Algebraic properties of classes of analytic functions, Seminars on Analytic Functions, Vol. II, pp. 175-188, Institute for Advanced Study, Princeton, N. J., 1957.
[4] K. de Leeuw, Banach spaces of Lipschitz functions, Studia Math. 21 (1961/1962), 55 – 66. · Zbl 0101.08901
[5] N. Dunford and J. Schwartz, Linear operators, Part I, Interscience, New York, 1958. · Zbl 0084.10402
[6] Georges Glaeser, Étude de quelques algèbres tayloriennes, J. Analyse Math. 6 (1958), 1 – 124; erratum, insert to 6 (1958), no. 2 (French). · Zbl 0091.28103 · doi:10.1007/BF02790231 · doi.org
[7] Lynn H. Loomis, An introduction to abstract harmonic analysis, D. Van Nostrand Company, Inc., Toronto-New York-London, 1953. · Zbl 0052.11701
[8] George W. Mackey, Commutative Banach algebras, Notas Mat. No. 17 (1959), 210. · Zbl 0086.31203
[9] H. Mirkil, Continuous translation of Hölder and Lipschitz functions, Canad. J. Math. 12 (1960), 674 – 685. · Zbl 0097.09702 · doi:10.4153/CJM-1960-060-3 · doi.org
[10] -, The work of Šilov on commutative semi-simple Banach algebras, Instituto de Matematica Pura e Aplicada do Conselho Nacional de Pesquisas, Rio de Janeiro, 1959.
[11] S. Myers, Differentiation in Banach algebras, Summary of lectures and seminars, pp. 135-137, Summer Institute on Set Theoretic Topology, Madison, Wis., 1955.
[12] Charles E. Rickart, General theory of Banach algebras, The University Series in Higher Mathematics, D. van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. · Zbl 0095.09702
[13] Laurent Schwartz, Théorie générale des fonctions moyenne-périodiques, Ann. of Math. (2) 48 (1947), 857 – 929 (French). · Zbl 0030.15004 · doi:10.2307/1969386 · doi.org
[14] G. E. Šilov, Homogeneous rings of functions, Amer. Math. Soc. Translation 1953 (1953), no. 92, 65.
[15] 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. · Zbl 0066.36103
[16] I. M. Singer and J. Wermer, Derivations on commutative normed algebras, Math. Ann. 129 (1955), 260 – 264. · Zbl 0067.35101 · doi:10.1007/BF01362370 · doi.org
[17] Hassler Whitney, On ideals of differentiable functions, Amer. J. Math. 70 (1948), 635 – 658. · Zbl 0037.35502 · doi:10.2307/2372203 · doi.org
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