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Higher point derivations on commutative Banach algebras. I. (English) Zbl 0364.46040


MSC:

46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
46J05 General theory of commutative topological algebras
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References:

[1] Badé, W. G.; Curtis, P. C., Homomorphisms of commutative Banach algebras, Amer. J. Math., 82, 851-866 (1960) · Zbl 0099.31903
[2] Badé, W. G.; Curtis, P. C., The continuity of derivations of Banach algebras, J. Functional Analysis, 16, 372-387 (1974) · Zbl 0296.46049
[3] W. G. Badé and P. C. Curtis, Jr.; W. G. Badé and P. C. Curtis, Jr.
[4] Bonsall, F. F.; Duncan, J., Complete Normed Algebras (1973), Springer-Verlag: Springer-Verlag New York · Zbl 0271.46039
[5] Dales, H. G., The uniqueness of the functional calculus, (Proc. London Math. Soc., 27 (1973)), 638-648, (3) · Zbl 0269.46038
[6] Dales, H. G.; McClure, J. P., Continuity of homomorphisms into certain commutative Banach algebras, (Proc. London Math. Soc., 26 (1973)), 69-81, (3) · Zbl 0244.46063
[7] Gulick, F., Systems of derivations, Trans. Amer. Math. Soc., 149, 465-488 (1970) · Zbl 0197.11102
[8] Heerema, N., Higher derivations and automorphisms of complete local rings, Bull. Amer. Math. Soc., 76, 1212-1225 (1970) · Zbl 0205.34404
[9] Loy, R. J., Continuity of higher derivations, (Proc. Amer. Math. Soc., 37 (1973)), 505-510 · Zbl 0252.46045
[10] Loy, R. J., Commutative Banach algebras with non-unique complete norm topology, Bull. Australian Math. Soc., 10, 409-420 (1974) · Zbl 0275.46044
[11] Nagel, A., Cohomology of sheaves of holomorphic functions satisfying boundary conditions on product domains, Trans. Amer. Math. Soc., 172, 133-141 (1972) · Zbl 0264.32005
[12] Scheinberg, S., Power series in one variable, J. Math. Anal. Appl., 31, 321-333 (1970) · Zbl 0216.16002
[13] Sherbert, D. R., The structure of ideals and point derivations in Banach algebras of Lipschitz functions, Trans. Amer. Math. Soc., 111, 240-272 (1964) · Zbl 0121.10204
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