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The existence of
discontinuous module derivations
Nicolas P. Jewell |
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Vol. 71 (1977), No. 2, 465–475
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Abstract |
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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
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Milestones
Received: 9 December 1976
Revised: 7 March 1977
Published: 1 August 1977
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Authors |
| Nicolas P. Jewell | |
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