We introduce an algebraic notion-stability-for an element of a commutative ring. It is shown that the stable elements of Banach algebras, and of Fréchet algebras, may be simply described. Part of the theory of power-series embeddings, given in [1] and [4], is seen to be of a purely algebraic nature. This approach leads to other natural questions.
@article{bwmeta1.element.bwnjournal-article-smv129i1p67bwm,
author = {Graham Allan},
title = {Stable elements of Banach and Fr\'echet algebras},
journal = {Studia Mathematica},
volume = {129},
year = {1998},
pages = {67-96},
zbl = {0909.46045},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv129i1p67bwm}
}
Allan, Graham. Stable elements of Banach and Fréchet algebras. Studia Mathematica, Tome 129 (1998) pp. 67-96. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv129i1p67bwm/
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