Approximately finite-dimensional Banach algebras are spectrally regular

作者：Bart Harm^*; Ehrhardt Torsten; Silbermann Bernd

来源：Linear Algebra and Its Applications, 2015, 470: 185-199.

DOI：10.1016/j.laa.2014.06.023

• Logarithmic residue
• AFD Banach algebra
• AF C*-algebra
• Irrational rotation algebra

Let B be a unital Banach algebra, which can in a certain sense be approximated by finite dimensional algebras. For instance, AF C*-algebras belong to this class. Further, let f be an analytic function on some bounded Cauchy domain Delta with values in B and suppose that the contour integral of the logarithmic derivative f'(lambda)f(-1)(lambda) along the positively oriented boundary partial derivative Delta vanishes (or is even only quasinilpotent). We prove that then f takes invertible values on all of Delta. This means that such Banach algebras are spectrally regular.

• 出版日期2015-4-1