Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



Unimodular matrices in Banach algebra theory

Authors: Gustavo Corach and Angel R. Larotonda
Journal: Proc. Amer. Math. Soc. 96 (1986), 473-477
MSC: Primary 46H05; Secondary 46M20
MathSciNet review: 822443
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

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

Article copyright: © Copyright 1986 American Mathematical Society