A semilattice structure for Arens products |
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Authors: | S. A. Hosseinioun A. Valadkhani |
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Affiliation: | 1. Department of Mathematics, University of Shahid Beheshti, Tehran, Iran
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Abstract: | Let (A,?) be a Banach algebra. Then for n∈?, 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 n∈?, we show that $P(A)=bigcup_{n=1}^{infty} P_{n}(A)$ is a ∧-semilattice. Also, we study P(A) as an infinite commutative semigroup and P(A)?{?} as a free semigroup generated by two elements. Then we investigate amenability and weak amenability for their semigroup Banach algebras. |
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