Vol. 77, No. 2, 1978

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The strong bidual of Γ(K)

Donald Curtis Taylor

Vol. 77 (1978), No. 2, 541–556

Let A be a C-algebra, K the Pedersen ideal of A, and Γ(K) the two-sided multipliers of K under the κ-topology. In this paper a study is made of the strong bidual of Γ(K), which we denote by Γ(K)′′. Here it is shown that the Arens products in Γ(K)′′ are well defined and coincide, and therefore make Γ(K)′′ a -algebra; moreover, if A is a PCS-algebra or has a σ-compact spectrum, it is shown that Γ(K)′′ is a metrizable b-algebra which is isometrically *-isomorphic to the Cartesian product of W-algebras.

Mathematical Subject Classification 2000
Primary: 46L05
Secondary: 46K05
Received: 26 July 1977
Published: 1 August 1978
Donald Curtis Taylor