Generators of maximal left ideals in Banach algebras
Functional Analysis
2012-09-18 v1
Abstract
In 1971, Grauert and Remmert proved that a commutative, complex, Noetherian Banach algebra is necessarily finite-dimensional. More precisely, they proved that a commutative, complex Banach algebra has finite dimension over whenever all the closed ideals in the algebra are (algebraically) finitely generated. In 1974, Sinclair and Tullo obtained a non-commutative version of this result. In 1978, Ferreira and Tomassini improved the result of Grauert and Remmert by showing that the statement is also true if one replaces `closed ideals' by `maximal ideals in the \v{S}ilov boundary of '. We shall give a shorter proof of this latter result, together with some extensions and related examples.
Keywords
Cite
@article{arxiv.1209.3530,
title = {Generators of maximal left ideals in Banach algebras},
author = {H. G. Dales and W. Żelazko},
journal= {arXiv preprint arXiv:1209.3530},
year = {2012}
}