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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Detalles Bibliográficos
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
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
Descripción
Sumario: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.

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