A Banach algebra  is said to be topologically left Noetherian (TLN) if for any increasing chain of closed left ideals  there exists an  such that  for all  We study some basic properties of this class of Banach algebras. In particular, we show that if  has an essential socle, then it is of finite dimension.

Banach algebra, topologically Noetherian, chain conditions.

Received: May 15, 2023; Accepted: July 5, 2023; Published: July 25, 2023

How to cite this article: M. Mabrouk and E. Saeed, Topologically Noetherian Banach algebras, JP Journal of Algebra, Number Theory and Applications 62(1) (2023), 1-11. http://dx.doi.org/10.17654/0972555523018

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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