Escaping a neighborhood along a prescribed sequence in Lie groups and Banach algebras
| Autor: | Sophie Grivaux, Catalin Badea, Vincent Devinck |
|---|---|
| Přispěvatelé: | Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Laboratoire de Mathématiques de Lens (LML), Université d'Artois (UA), Centre National de la Recherche Scientifique (CNRS), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), ANR-17-CE40-0021,FRONT2017,Frontières de la théorie des opérateurs(2017) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
General Mathematics
Group Theory (math.GR) [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] 01 natural sciences [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR] Combinatorics Identity (mathematics) Mathematics - Metric Geometry 0103 physical sciences FOS: Mathematics Topological group 0101 mathematics [MATH]Mathematics [math] Eigenvalues and eigenvectors Mathematics Sequence Normed algebra 47A10 47A12 47A60 22E15 010102 general mathematics Lie group Metric Geometry (math.MG) 16. Peace & justice Functional Analysis (math.FA) Mathematics - Functional Analysis Unimodular matrix 010307 mathematical physics Mathematics - Group Theory Group theory |
| Zdroj: | Canadian Mathematical Bulletin Canadian Mathematical Bulletin, 2020, 63 (3), pp.484-505 Canadian Mathematical Bulletin, 2020, 63 (3), pp.484-505. ⟨10.4153/S0008439519000560⟩ |
| ISSN: | 0008-4395 1496-4287 |
| DOI: | 10.4153/S0008439519000560⟩ |
| Popis: | It is shown that Jamison sequences, introduced in 2007 by Badea and Grivaux ([C. Badea and S. Grivaux, Unimodular eigenvalues, uniformly distributed sequences and linear dynamics, Adv. Math. 211 (2007), no. 2, 766--793]), arise naturally in the study of topological groups with no small subgroups, of Banach or normed algebra elements whose powers are close to identity along subsequences, and in characterizations of (self-adjoint) positive operators by the accretiveness of some of their powers. The common core of these results is a description of those sequences for which non-identity elements in Lie groups or normed algebras escape an arbitrary small neighborhood of the identity in a number of steps belonging to the given sequence. Several spectral characterizations of Jamison sequences are given and other related results are proved. Comment: 25 pages; suggestions by two referees have been taken into account |
| Databáze: | OpenAIRE |
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