Some aspects of \(\lambda (P_0,\mathbb{N})\)-nuclearity
type: Item
instance of: scholarly article
zbMATH Open document ID: 1007.46001
author: G. M. Deheri
publication date: 2002-12-26T00:00:00Z
full work available at URL: https://eudml.org/doc/38645
Mathematics Subject Classification ID: 46A11
Mathematics Subject Classification ID: 46A35
Mathematics Subject Classification ID: 46A45
zbMATH DE Number: 1623554
zbMATH Keywords: nuclear spaces
zbMATH Keywords: Köthe sequence spaces
zbMATH Keywords: bases
zbMATH Keywords: Kolmogorov \(i\)-diameters
MaRDI profile type: Publication
title: Some aspects of \(\lambda (P_0,\mathbb{N})\)-nuclearity
published in: Extracta Mathematicae
review text: The author proves a criterion for \(\lambda (P_0 ; \mathbb{N}) \)-nuclearity of generalized Köthe spaces \(\lambda_\mu (P) \) and of locally convex topological vector spaces with generalized bases. NEWLINENEWLINENEWLINEWe recall that, given \(P_0 = \{(b^k_i): k\geq 1 \} \) a stable countable nuclear power set of infinite type, a locally convex space \(E\) with a basis \(U_0\) of absolutely convex neighborhoods of zero is said to be \(\lambda (P_0 ; \mathbb{N}) \)-nuclear if for every \(k\geq 1 \) and \(U \in U_0 \) there exists \(V \in U_0 \) (\(V\subset U\)) such that \( (b^k_i d_i (V,U)) \in \ell^\infty ,\) where \(d_i (V,U) \) are the Kolmogorov \(i\)-diameters.
reviewed by: A. Peris
description: scientific article; zbMATH DE number 1623554