Difference between revisions of "Complete set of functionals"
From Encyclopedia of Mathematics
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| − | A set | + | A set $\Gamma$ of continuous linear functionals $f(x)$, defined on a linear topological space $X$, such that there is no element $x\in X$, $x\neq0$, on which the equality $f(x)=0$ is satisfied for all $f\in\Gamma$. Every locally convex space has a complete set of functionals. |
Latest revision as of 15:01, 8 August 2014
total set of functionals
A set $\Gamma$ of continuous linear functionals $f(x)$, defined on a linear topological space $X$, such that there is no element $x\in X$, $x\neq0$, on which the equality $f(x)=0$ is satisfied for all $f\in\Gamma$. Every locally convex space has a complete set of functionals.
How to Cite This Entry:
Complete set of functionals. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Complete_set_of_functionals&oldid=16190
Complete set of functionals. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Complete_set_of_functionals&oldid=16190
This article was adapted from an original article by M.I. Kadets (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article