Set quantities and Tauberian operators
type: Item
instance of: scholarly article
title: Set quantities and Tauberian operators
zbMATH Open document ID: 1028.46009
DOI: 10.1155/S1085337501000641
author: Sergio Falcon
author: K. Sadarangani
published in: Abstract and Applied Analysis
publication date: 2004-01-26T00:00:00Z
full work available at URL: https://eudml.org/doc/50479
review text: Summary: The concept of convexity plays an important role in the classical geometry of normed spaces and it is frequently used in several branches of nonlinear analysis. In recent years some papers that contain generalizations of the concept of convexity with the help of measures of noncompactness have appeared. The Tauberian operators were introduced by \textit{N. Kalton} and \textit{A. Wilansky} [Proc. Am. Math. Soc. 57, 251-255 (1976; Zbl 0304.47023)] and they appear in the literature with the aim of responding to some questions related to the summability and the factorization of operators; in the preservation by isomorphisms in Banach spaces, and so forth. In this paper we make the study of the Tauberian operators, not starting from the Euclidean distance, but by means of general set quantities.
Mathematics Subject Classification ID: 46A25
Mathematics Subject Classification ID: 46B10
Mathematics Subject Classification ID: 46A50
zbMATH DE Number: 1750238
zbMATH Keywords: measures of noncompactness
zbMATH Keywords: Tauberian operators
MaRDI profile type: Publication
OpenAlex ID: W2081666622
description: scientific article; zbMATH DE number 1750238