Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Unimodular matrices in Banach algebra theory
HTML articles powered by AMS MathViewer

by Gustavo Corach and Angel R. Larotonda PDF
Proc. Amer. Math. Soc. 96 (1986), 473-477 Request permission

Abstract:

Let $A$ be a ring with 1 and denote by $L$ (resp. $R$) the set of left (resp. right) invertible elements of $A$. If $A$ has an involution *, there is a natural bijection between $L$ and $R$. In general, it seems that there is no such bijection; if $A$ is a Banach algebra, $L$ and $R$ are open subsets of $A$, and they have the same cardinality. More generally, we prove that the spaces ${U_k}({A^n})$ of $n \times k$-left-invertible matrices and $_kU({A^n})$ of $k \times n$-right-invertible matrices are homotopically equivalent. As a corollary, we answer negatively two questions of Rieffel [12].
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46H05, 46M20
  • Retrieve articles in all journals with MSC: 46H05, 46M20
Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 96 (1986), 473-477
  • MSC: Primary 46H05; Secondary 46M20
  • DOI: https://doi.org/10.1090/S0002-9939-1986-0822443-7
  • MathSciNet review: 822443