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...
Guardado en:
Autores principales: | , |
---|---|
Formato: | JOUR |
Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00029939_v96_n3_p473_Corach |
Aporte de: |
id |
todo:paper_00029939_v96_n3_p473_Corach |
---|---|
record_format |
dspace |
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 |
_version_ |
1807318371509731328 |