An extremal problem in Banach algebras
We study asymptotics of a class of extremal problems $r_n(A,\varepsilon )$ 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 . 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  is answered in the negative.