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Zbl 0758.15007
Ding, Lifeng
Separating vectors and reflexivity. (English)
[J] Linear Algebra Appl. 174, 37-52 (1992). ISSN 0024-3795

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.\par 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.
[G.P.Barker (Kansas City)]

MSC 2000:: *15A30 Algebraic systems of matrices
15A60 Appl. of functional analysis to matrix theory
15A04 Linear transformations (linear algebra)

Keywords: space of linear transformations; algebraically reflexive sets; vector space; separating vectors; reflexivity

Cited in: Zbl 1111.47061

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