Geodesic
Central Double Centralizers on Quasi-Central Banach Algebras with Bounded Approximate Identity
Canadian journal of mathematics, Tome 35 (1983) no. 2, pp. 373-384

Voir la notice de l'article provenant de la source Cambridge University Press

We assume throughout this paper that A is a semi-simple, quasi-central, complex Banach algebra with a bounded approximate identity {eα }. The author [6] has shown that every central double centralizer T on A can be, under suitable conditions, represented as a bounded continuous complex-valued function ΦT on Prim A, the structure space of A with the hull-kernel topology, such that Here x + P for P ∊ Prim A denotes the canonical image of x in A/P. This map Φ is called Dixmier's representation of Z(M(A)), the central double centralizer algebra of A. We denote by τ the canonical isomorphism of A into the Banach algebra D(A) with the restricted Arens product as defined in [6]. Also denote by μ Davenport's representation of Z(M(A)). In fact, this map μ is given by for each T ∊ Z(M(A)). 
Central Double Centralizers on Quasi-Central Banach Algebras with Bounded Approximate Identity. Canadian journal of mathematics, Tome 35 (1983) no. 2, pp. 373-384. doi: 10.4153/CJM-1983-021-0
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