A semilattice structure for Arens products

作者：Hosseinioun S A^*; Valadkhani A

来源：Semigroup Forum, 2013, 87(2): 428-436.

DOI：10.1007/s00233-013-9479-6

• Banach algebra
• Arens products
• Semilattice
• Semigroup
• Amenability
• Weak amenability

Let (A,a <...) be a Banach algebra. Then for naa"center dot, A ((2n)) has 2 (n) Arens products. In this paper we study the relations between the Arens products on A ((2n)). Moreover, if P (n) (A) denotes the set of all Arens products on A ((2n)), for naa"center dot, we show that is a a -semilattice. Also, we study P(A) as an infinite commutative semigroup and P(A)-{a <...} as a free semigroup generated by two elements. Then we investigate amenability and weak amenability for their semigroup Banach algebras.

• 出版日期2013-10