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In mathematics, specifically in order theory and functional analysis, a locally convex vector lattice (LCVL) is a topological vector lattice that is also a locally convex space. LCVLs are important in the theory of topological vector lattices.
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6875
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Let be an order complete vector lattice w … Let be an order complete vector lattice with a regular order. The following are equivalent:
is of minimal type.
For every majorized and direct subset of the section filter of converges in when is endowed with the order topology.
Every order convergent filter in converges in when is endowed with the order topology.
Moreover, if is of minimal type then the order topology on is the finest locally convex topology on for which every order convergent filter converges.h every order convergent filter converges.
, Suppose that is an order complete locally … Suppose that is an order complete locally convex vector lattice with topology and endow the bidual of with its natural topology and canonical order . The following are equivalent:
The evaluation map induces an isomorphism of with an order complete sublattice of
For every majorized and directed subset of the section filter of converges in .
Every order convergent filter in converges in .rder convergent filter in converges in .
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Corollary
, Theorem
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| rdfs:comment |
In mathematics, specifically in order theory and functional analysis, a locally convex vector lattice (LCVL) is a topological vector lattice that is also a locally convex space. LCVLs are important in the theory of topological vector lattices.
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| rdfs:label |
Locally convex vector lattice
|
