An extremal problem in Banach algebras
Volume 145 / 2001
Studia Mathematica 145 (2001), 255-264
MSC: Primary 46J05; Secondary 42A20.
DOI: 10.4064/sm145-3-5
Abstract
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 [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.
