J Austral Math Soc Ser A 56 pp303--313, 1994.

The Second Dual od C₀(S, A)

Stephen T. L. Choy and James C. S. Wong

Abstract

The second dual of the vector-valued function space C₀(S, A) is characterized in terms of generalized functions in the case where A* and A** have the Radon-Nikodym property. As an application we present a simple proof that C₀(S, A) is Arens regular if and only if A is Arens regular in this case. A representation theorem of the measure mh is given, where m Î C₀*(S, A), h Î L_¥ (|m|, A**) and mh is defined by the Arens product.

1991 AMS Subject Classification: 46G10, 46J10

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Authors

Stephen T. L. Choy

National University of Singapore, Republic of Singapore.

James C. S. Wong

The University of Calgary, Canada, T2N 1N4.