# Positive Linear Forms Vanish on the Radical

Positive Linear Forms Vanish on the Radical If A is a complex *-algebra with unit then every linear form L on A which is positive in the sense that $$L(a*a) \geqslant 0$$ for all $$a \in A$$ vanishes on the Jacobson radical of A. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Positive Linear Forms Vanish on the Radical

, Volume 4 (2) – Oct 25, 2004
4 pages

Publisher
Springer Journals
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1023/A:1009861822481
Publisher site
See Article on Publisher Site

### Abstract

If A is a complex *-algebra with unit then every linear form L on A which is positive in the sense that $$L(a*a) \geqslant 0$$ for all $$a \in A$$ vanishes on the Jacobson radical of A.

### Journal

PositivitySpringer Journals

Published: Oct 25, 2004

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