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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Extension problem to an invertible matrix
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by Vadim Tolokonnikov PDF
Proc. Amer. Math. Soc. 117 (1993), 1023-1030 Request permission

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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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 117 (1993), 1023-1030
  • MSC: Primary 46J15; Secondary 30H05, 47A57, 47D99
  • DOI: https://doi.org/10.1090/S0002-9939-1993-1123668-X
  • MathSciNet review: 1123668