Unimodular matrices in banach algebra theory

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 hav...

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Autores principales: Corach, G., Larotonda, A.R.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00029939_v96_n3_p473_Corach
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spelling todo:paper_00029939_v96_n3_p473_Corach2023-10-03T13:55:20Z Unimodular matrices in banach algebra theory Corach, G. Larotonda, A.R. 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 Uk(An) of n X k-left-invertible matrices and kU(An) of k X n-right-invertible matrices are homotopically equivalent. As a corollary, we answer negatively two questions of Rieffel. © 1986 American Mathematical Society. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00029939_v96_n3_p473_Corach
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description 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 Uk(An) of n X k-left-invertible matrices and kU(An) of k X n-right-invertible matrices are homotopically equivalent. As a corollary, we answer negatively two questions of Rieffel. © 1986 American Mathematical Society.
format JOUR
author Corach, G.
Larotonda, A.R.
spellingShingle Corach, G.
Larotonda, A.R.
Unimodular matrices in banach algebra theory
author_facet Corach, G.
Larotonda, A.R.
author_sort Corach, G.
title Unimodular matrices in banach algebra theory
title_short Unimodular matrices in banach algebra theory
title_full Unimodular matrices in banach algebra theory
title_fullStr Unimodular matrices in banach algebra theory
title_full_unstemmed Unimodular matrices in banach algebra theory
title_sort unimodular matrices in banach algebra theory
url http://hdl.handle.net/20.500.12110/paper_00029939_v96_n3_p473_Corach
work_keys_str_mv AT corachg unimodularmatricesinbanachalgebratheory
AT larotondaar unimodularmatricesinbanachalgebratheory
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