Abstract

Amenability of Pseudo Complete Locally Convex Algebras

S.A. Ayinde, A.K. Adio, R.U. Kanu

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Abstract We extend the notion of amenable Banach algebras to pseudo-complete locally convex algebra ?, where ? is considered as a direct limit of inductive system of Banach algebras. We endowed ? with a strict inductive limit topology. In line with this, derivation on ? is shown to be continuous. Consequent upon this and also base on the existence of both the locally bounded approximate identity (????) and locally bounded approximate diagonal (????) in ?, we show that ? is amenable. Keywords: Pseudo-complete locally convex algebras, Continuous derivation, Locally bounded approximate identity, Locally bounded approximate diagonal, Amenability. 2020 Mathematics Subject Classification. 46H99

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