Some more Steinhaus type theorems over valued fields
type: Item
instance of: scholarly article
title: Some more Steinhaus type theorems over valued fields
zbMATH Open document ID: 0943.47058
author: P. N. Natarajan
published in: Annales Mathématiques Blaise Pascal
publication date: 2000-08-28T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/79207
review text: Let \(A\) be an infinite matrix with entries from a complete non-trivially valued non-Archimedean field. The author finds necessary and sufficient conditions for \(A\) to define a bounded operator between various sequence spaces: \(\ell\to c_0\), \(c\to c_0\), \(\ell_\infty \to c_0\), and also for the relation \[ \sum\limits_{n=0}^\infty (Ax)_n=\sum\limits_{k=0}^\infty x_k,\quad x=(x_k)\in \ell. \] The latter problem is studied also for \(K=\mathbb R\) or \(\mathbb C\).
Mathematics Subject Classification ID: 47S10
Mathematics Subject Classification ID: 47B37
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 40H05
zbMATH DE Number: 1331690
zbMATH Keywords: sequence space
zbMATH Keywords: infinite matrix
zbMATH Keywords: Steinhaus theorem
reviewed by: Anatoly N. Kochubei
MaRDI profile type: Publication
OpenAlex ID: W4230947229
cites work: Q5587233
cites work: Q4858391
cites work: On Theorems of Steinhaus Type
cites work: Q4185266
cites work: Some Steinhaus type theorems over valued fields
cites work: Matrixtransformationen von Folgenräumen. Eine Ergebnisübersicht
DOI: 10.5802/AMBP.114
description: scientific article; zbMATH DE number 1331690