Embedding Nilpotent Finite Dimensional Banach Algebras into Amenable Banach Algebras

✍ Scribed by Niels Grønbæk; George A. Willis

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 307 KB
• Volume: 145
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1996.3025

✦ Synopsis

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 hull is a set of non-synthesis.