Vol. 71, No. 2, 1977

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The existence of discontinuous module derivations

Nicolas P. Jewell

Vol. 71 (1977), No. 2, 465–475
Abstract

In this paper it is shown that if a commutative Banach algebra B with identity has a maximal ideal M whose algebraic powers M2,M3, form a descending chain of ideals which never becomes constant then there exists a discontinuous module derivation from B into a Banach-B-bimodule. This fact is linked with the known sufficient conditions for every module derivation from B to be continuous when B is separable. Some examples are given to demonstrate unusual behaviour in such chains of ideals in particular situations.

Mathematical Subject Classification 2000
Primary: 46J05
Milestones
Received: 9 December 1976
Revised: 7 March 1977
Published: 1 August 1977
Authors
Nicolas P. Jewell