We study asymptotics of a class of extremal problems rₙ(A,ε) related to norm controlled inversion in Banach algebras. In a general setting we prove estimates that can be considered as quantitative refinements of a theorem of Jan-Erik Björk [1]. In the last section we specialize further and consider a class of analytic Beurling algebras. In particular, a question raised by Jan-Erik Björk in [1] is answered in the negative.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm145-3-5,
author = {Anders Olofsson},
title = {An extremal problem in Banach algebras},
journal = {Studia Mathematica},
volume = {147},
year = {2001},
pages = {255-264},
zbl = {1013.46041},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm145-3-5}
}
Anders Olofsson. An extremal problem in Banach algebras. Studia Mathematica, Tome 147 (2001) pp. 255-264. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm145-3-5/