Approximate amenability is not bounded approximate amenability

作者：Ghahramani F^*; Read C J

来源：Journal of Mathematical Analysis and Applications, 2015, 423(1): 106-119.

DOI：10.1016/j.jmaa.2014.09.060

• Approximately amenable Banach algebra
• Approximate diagonal
• Boundedly approximately amenable
• Banach algebras
• Approximate identity

We obtain a new criterion sufficient for approximate amenability of Banach algebras, and an associated criterion sufficient for approximate amenability of co-direct sums of approximately amenable Banach algebras. We use these criteria to give examples of Banach algebras which are approximately amenable, but not boundedly approximately amenable. Thus we answer a question which was open since the year 2004. This is, so to speak, the complementary result to one of our earlier ones in the paper [F. Ghahramani, C.J. Read, Approximate identities in approximate amenability, J. Funct. Anal. 262 (9) (2012) 3929-3945], where we gave examples of boundedly approximately amenable Banach algebras that are not boundedly approximately contractible.

• 出版日期2015-3-1