ordered topological vector space

Let k be either or considered as a field. An ordered topological vector space L, (ordered t.v.s for short) is

The last statement can be interpreted as follows: if a sequence of non-negative elements xi of L converges to an element x, then x is non-negative.

Remark. Let L,M be two ordered t.v.s., and f:LM a linear transformation that is monotone. Then if 0xL, 0f(x)M also. Therefore f(L+)M+. Conversely, a linear map that is invariantMathworldPlanetmath under positive cones is monotone.

Title ordered topological vector space
Canonical name OrderedTopologicalVectorSpace
Date of creation 2013-03-22 17:03:23
Last modified on 2013-03-22 17:03:23
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 4
Author CWoo (3771)
Entry type Definition
Classification msc 06F20
Classification msc 46A40
Classification msc 06F30
Synonym ordered topological linear space