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Higher point derivations on commutative Banach algebras, I

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>10/1977
<mark>Journal</mark>Journal of Functional Analysis
Issue number2
Volume26
Number of pages24
Pages (from-to)166-189
<mark>State</mark>Published
<mark>Original language</mark>English

Abstract

A higher point derivation on a commutative algebra is a finite or infinite sequence of linear functionals connected by the condition that they satisfy the Leibnitz identities. We discuss here higher point derivations on commutative Banach algebras. We study the extent to which point derivations are automatically continuous, and, for certain Banach algebras, we consider the maximum possible order of a higher point derivation. In particular, we obtain a complete description of the order and continuity properties of higher point derivations on the Banach algebra of n-times continuously differentiable functions on the unit interval.