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Extension problem to an invertible matrix

Author: Vadim Tolokonnikov
Journal: Proc. Amer. Math. Soc. 117 (1993), 1023-1030
MSC: Primary 46J15; Secondary 30H05, 47A57, 47D99
MathSciNet review: 1123668
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Abstract: The extension problem for rectangular matrices with values in Banach algebra to an invertible square matrix is investigated. For this problem to be solvable for a matrix $ D$, the following condition is necessary: for every maximal ideal $ m$ of the algebra, the numerical matrix $ D(m)$ must have maximal rank. This condition is sufficient for many algebras, for example, for the algebras $ {H^\infty }(R)$ of bounded analytic functions in a plane finitely connected domain $ R$ and to Sarason subalgebras in the algebra $ {H^\infty }$.

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Keywords: Banach algebras, subalgebras of $ {H^\infty }$, matrices, projective modules, vector bundles
Article copyright: © Copyright 1993 American Mathematical Society