Sequences of operators in Köthe-Toeplitz duals
type: Item
instance of: scholarly article
title: Sequences of operators in Köthe-Toeplitz duals
zbMATH Open document ID: 0954.46039
author: Bhagavathy Jayaraman
published in: The Journal of Analysis
publication date: 2001-02-14T00:00:00Z
review text: Let \(X\) and \(Y\) denote non-Archimedean Banach spaces over a complete nontrivially non-Archimedean valued field \(K\) and \(B(X,Y)\) the Banach algebra of bounded linear operators from \(X\) to \(Y\) with the operator norm. The following result is established among others: Let \(S\) be the set of all sequences \(\{T_k\}\) such that the group norm is finite. Then \(S\) is a non-Archimedean Banach space with the natural operations under the norm \(\|\{T_k\}\|\). Let \(\{A_k\}\) be a sequence of operators from \(X\) to \(Y\). Characterizations for \(\{A_k\}\) to belong to \(\alpha\) and \(\beta\) duals of \(X\)-valued sequence spaces \(c_0(X)\), \(c(X)\), \(\ell_\infty(X)\) and \(\ell_p(X)\) with \(1\leq p<\infty\) are also given.
Mathematics Subject Classification ID: 46S10
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 46B28
zbMATH DE Number: 1417953
zbMATH Keywords: Köthe-Toeplitz duals
zbMATH Keywords: non-Archimedean Banach spaces
zbMATH Keywords: Banach algebra of bounded linear operators
zbMATH Keywords: group norm
zbMATH Keywords: \(\alpha\) and \(\beta\) duals of \(X\)-valued sequence spaces
reviewed by: K. Chandrasekhara Rao
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1417953