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 ${H^\infty }$.References
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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