Separating vectors and reflexivity
type: Item
instance of: scholarly article
title: Separating vectors and reflexivity
zbMATH Open document ID: 0758.15007
DOI: 10.1016/0024-3795(92)90040-H
author: Lifeng Ding
published in: Linear Algebra and its Applications
publication date: 1992-10-26T00:00:00Z
review text: Let \(V\) be a vector space over a field \(F\), and let \(S\) be a subspace of the space of all linear transformations on \(V\). A vector \(x\in V\) is said to separate \(S\) in case the map sending \(s\) to \(sx\) is injective for all \(s\in S\). This present paper clarifies the connection between separating vectors and reflexivity. The main result of the paper gives conditions under which the existence of separating vectors for a subspace implies that the subspace is algebraically reflexive.
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15A04
zbMATH DE Number: 69518
zbMATH Keywords: space of linear transformations
zbMATH Keywords: algebraically reflexive sets
zbMATH Keywords: vector space
zbMATH Keywords: separating vectors
zbMATH Keywords: reflexivity
reviewed by: George Phillip Barker
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 69518