Amenability of Pseudo Complete Locally Convex Algebras

Amenability of Pseudo Complete Locally Convex Algebras

Author by Dr. Semiu Ayinde

Journal/Publisher: Abacus (mathematics Science Series)

Volume/Edition: 49

Language: English

Pages: 7 - 19

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.


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