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Higher point derivations on commutative Banach algebras, III

Published online by Cambridge University Press:  20 January 2009

H. G. Dales  and
J. P. McClure
H. G. Dales
Affiliation:
School of MathematicsUniversity of LeedsLeeds, LS2 9JT, England
J. P. McClure
Affiliation:
Department of Mathematics and AstronomyUniversity of ManitobaWinnipeg, R3T 2N2, Canada
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Let A be a commutative Banach algebra with identity 1 over the complex field C, and let d0 be a character on A. We recall that a (higher) point derivation of order q on A at d0 is a sequence d1, …, dq of linear functionals on A such that the identities

hold for each choice of f and g in A and k in {1, …, q}. A point derivation of infinite order is an infinite sequence {dk} of linear functionals such that (1.1) holds for all k. A point derivation is continuous if each dk is continuous, totally discontinuous if dk is discontinuous for each k≧1, and degenerate if d1 = 0.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 24 , Issue 1 , February 1981 , pp. 31 - 40
Copyright
Copyright © Edinburgh Mathematical Society 1981

References

REFERENCES

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