On the Arens product and approximate identity in locally convex algebras

Abbas Zivari-kazempour


Let A' and A" be the dual and bidual spaces of a locally convex algebra A with dual and weak* topology, respectivly. In this paper we show that A has a bounded right (left) approximate identity if and only if A" has a right (left) unit with respect to the first (second) Arens product.

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