Derivations on commutative normed algebras.

*(English)*Zbl 0067.35101##### Keywords:

functional analysis##### References:

[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). |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.