Topological algebras with subadditive boundedness radius
Abstract Let A be a topological algebra and β a subadditive boundedness radius on A. In this paper we show that β is, under certain conditions, automatically submultiplicative. Then we apply this fact to prove that the spectrum of any element of A is non-empty. Finally, in the case...
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| Autores principales: | , |
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| Lenguaje: | English |
| Publicado: |
Universidad de La Frontera. Departamento de Matemática y Estadística.
2020
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462020000300289 |
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| Sumario: | Abstract Let A be a topological algebra and β a subadditive boundedness radius on A. In this paper we show that β is, under certain conditions, automatically submultiplicative. Then we apply this fact to prove that the spectrum of any element of A is non-empty. Finally, in the case when A is a normed algebra, we compare the initial normed topology with the normed topology τβ, induced by β on A, where β−1(0) = 0. |
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