# On Separation of Points from Additive Subgroups of Banach Spaces by Continuous Characters and Positive Definite Functions

On Separation of Points from Additive Subgroups of Banach Spaces by Continuous Characters and... Let G be an additive subgroup of a normed space X. We say that a point $$x\in X\setminus G$$ is weakly separated (resp. $$\mathcal P$$ -separated) from G if it can be separated from G by a continuous character (resp. by a continuous positive definite function). Let T : X → Y be a continuous linear operator. Consider the following conditions: http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# On Separation of Points from Additive Subgroups of Banach Spaces by Continuous Characters and Positive Definite Functions

, Volume 12 (2) – Jan 11, 2008
28 pages

Publisher
Springer Journals
Subject
Mathematics; Econometrics; Calculus of Variations and Optimal Control; Optimization; Potential Theory; Operator Theory; Fourier Analysis
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-007-2009-6
Publisher site
See Article on Publisher Site

### Abstract

Let G be an additive subgroup of a normed space X. We say that a point $$x\in X\setminus G$$ is weakly separated (resp. $$\mathcal P$$ -separated) from G if it can be separated from G by a continuous character (resp. by a continuous positive definite function). Let T : X → Y be a continuous linear operator. Consider the following conditions:

### Journal

PositivitySpringer Journals

Published: Jan 11, 2008

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