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Derivations on commutative normed algebras

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Literatur

  1. Silov showed in his paper “On a property of rings of functions”, Doklady Akad. Nauk SSSR. (N.S.) 58, 985–988 (1947), that the algebra of all infinitely differentiable functions on an interval cannot be normed so as to be a Banach algebra. Prof.I. Kaplansky conjectured that the “reason” for this was that non-zero derivations could not exist on a commutative semisimple Banach algebra. Theorem 1 proves this conjecture for bounded derivations. It seems probable that hypothesis (iv) is superfluous.

  2. SeeChevalley: “Theory of Lie Groups”, p. 137. Princeton Univ. Press. (1946).

  3. Originally proved bySilov, cf. footnote 1).

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Authors and Affiliations

  1. New York City

    I. M. Singer & J. Wermer

  2. Providence, Rhode Island

    I. M. Singer & J. Wermer

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  1. I. M. Singer
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  2. J. Wermer
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Singer, I.M., Wermer, J. Derivations on commutative normed algebras. Math. Ann. 129, 260–264 (1955). https://doi.org/10.1007/BF01362370

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