Banach halos and short isometries - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2022

Banach halos and short isometries

Tomoki Mihara
  • Fonction : Auteur
  • PersonId : 1183959

Résumé

The aim of this article is twofold. First, we develop the notion of a Banach halo, similar to that of a Banach ring, except that the usual triangular inequality is replaced by the inequality $|a + b| \leq (|a| , |b|)_p$ involving the p-norm for some $p \in]0, +∞]$, or by the inequality $|a+b|\leq C\max(|a|,|b|)$. This allows us to have a flow of powers on Banach halos and to work, e.g., with the square of the usual absolute value on $\Z$. Then we define and study the group of short isometries of normed involutive coalgebras over a base commutative Banach halo. An aim of this theory is to define a representable group $K_n\subset GL_n$ whose points with values in $\R$ give $O_n(\R)$ and whose points with values in $\Q_p$ give $\GL_n(\Z_p)$, giving to the analogy between these two groups a kind of geometric explanation.
Fichier principal
Vignette du fichier
short-isometries.pdf (315.53 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03845029 , version 1 (09-11-2022)

Identifiants

Citer

Tomoki Mihara, Frédéric Paugam. Banach halos and short isometries. 2022. ⟨hal-03845029⟩
10 Consultations
2 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More