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1992•Glasgow Mathematical JournalOpen access

A functorial approach to weak amenability for commutative Banach algebras

Volker Runde

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Abstract

Let A be a commutative algebra, and let M be a bimodule over A. A derivation from A into M is a linear mapping D: A→M that satisfies If M is only a left A-module, by a derivation from A into M we mean a linear mapping D: A→M such that Each A-bimodule M is trivially a left module. However, unless it is commutative, i.e. the two classes of linear operators from A into M characterized by (1) and (2), respectively, need not coincide.

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Let A be a commutative algebra, and let M be a bimodule over A. A derivation from A into M is a linear mapping D: A→M that satisfies If M is only a left A-module, by a derivation from A into M we mean a linear mapping D: A→M such that Each A-bimodule M is trivially a left module. However, unless it is commutative, i.e. the two classes of linear operators from A into M characterized by (1) and (2), respectively, need not coincide.

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Available abstract

Let A be a commutative algebra, and let M be a bimodule over A. A derivation from A into M is a linear mapping D: A→M that satisfies If M is only a left A-module, by a derivation from A into M we mean a linear mapping D: A→M such that Each A-bimodule M is trivially a left module. However, unless it is commutative, i.e. the two classes of linear operators from A into M characterized by (1) and (2), respectively, need not coincide.

Key concepts: Bimodule, Mathematics, Commutative property, Pure mathematics, Banach algebra, Algebra over a field, Discrete mathematics, Banach space

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