We prove that any finite dimensional nilpotent commutative Banach algebra can be embedded isometrically into a commutative amenable Banach algebra, whose approximate diagonal is bounded by one. This amenable algebra is constructed by means of a quotient of a Fourier algebra by a closed ideal, whose
Amenable Banach algebras
β Scribed by A. Ya. Khelemskii; M. V. Sheinberg
- Publisher
- Springer US
- Year
- 1979
- Tongue
- English
- Weight
- 581 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0016-2663
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We investigate amenable and weakly amenable Banach algebras with compact multiplication. Any amenable Banach algebra with compact multiplication is biprojective. As a consequence, every semisimple such algebra which has the approximation property is a topological direct sum of full matrix algebras.
Recent work by various authors has considered the implications of Banach algebra amenability for various algebras defined over locally compact groups, one of the basic tools being the fact that a continuous homomorphic image of an amenable algebra is again amenable. In the present paper we look at t