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We study asymptotics of a class of extremal problems rn(A;") related to norm controlled inversion in Banach algebras. In a general setting we prove estimates that can be considered as quantitative renemen ts of a theorem of Jan-Erik Bjork (1). In the last section we specialize further and consider a class of analytic Beurling algebras. In particular, a question raised by Jan-Erik Bjork in (1) is answered in the negative.

An extremal problem in Banach algebras