Vol. 68, No. 1, 1977

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Continuity of module and higher derivations

Nicolas P. Jewell

Vol. 68 (1977), No. 1, 91–98

In this paper it is shown that derivations from L1[0,1] into Banach-L1[0,1]-modules are automatically continuous. The result is obtained as a corollary of a theorem in which sufficient conditions on the closed ideals of a separable commutative Banach algebra B are given so that every module derivation from B into a Banach-B-bimodule is continuous. One of the conditions obtained is best possible. For the general case of a Banach algebra A (not necessarily commutative or separable) sufficient conditions on the closed ideals are also given to force the continuity of module derlvations and of certain higher derivations from any Banach algebra onto A.

Mathematical Subject Classification 2000
Primary: 46H05
Received: 25 March 1976
Published: 1 January 1977
Nicolas P. Jewell