Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Higher point derivations on commutative Banach algebras, I
AU - Dales, H.G.
AU - McClure, J. P.
PY - 1977/10
Y1 - 1977/10
N2 - 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.
AB - 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.
U2 - 10.1016/0022-1236(77)90009-X
DO - 10.1016/0022-1236(77)90009-X
M3 - Journal article
VL - 26
SP - 166
EP - 189
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 2
ER -