Let (𝑋,𝑋+) be a quasi ordered ∗-vector space with order unit, that is, a ∗-vector space 𝑋 with order unite together with a cone 𝑋+⊆𝑋. Our main goal is to find a condition weaker than properness of 𝑋, which suffices for fundamental results of ordered vector space theory to work. We show that having a non-empty state space or equivalently having a non-negative order unit is a suitable replacement for properness of 𝑋+. At first, we examine real vector spaces and then the complex case. Then we apply the results to self adjoint unital subspaces of unital ∗-algebras to find direct and shorter proofs of some of the existing results in the literature.
Esslamzadeh, G. H. , Moazami Goodarzi, M. and Taleghani, F. (2014). Structure of quasi ordered ∗-vector spaces. Iranian Journal of Science, 38(4), 445-453. doi: 10.22099/ijsts.2014.2561
MLA
Esslamzadeh, G. H. , , Moazami Goodarzi, M. , and Taleghani, F. . "Structure of quasi ordered ∗-vector spaces", Iranian Journal of Science, 38, 4, 2014, 445-453. doi: 10.22099/ijsts.2014.2561
HARVARD
Esslamzadeh, G. H., Moazami Goodarzi, M., Taleghani, F. (2014). 'Structure of quasi ordered ∗-vector spaces', Iranian Journal of Science, 38(4), pp. 445-453. doi: 10.22099/ijsts.2014.2561
CHICAGO
G. H. Esslamzadeh , M. Moazami Goodarzi and F. Taleghani, "Structure of quasi ordered ∗-vector spaces," Iranian Journal of Science, 38 4 (2014): 445-453, doi: 10.22099/ijsts.2014.2561
VANCOUVER
Esslamzadeh, G. H., Moazami Goodarzi, M., Taleghani, F. Structure of quasi ordered ∗-vector spaces. Iranian Journal of Science, 2014; 38(4): 445-453. doi: 10.22099/ijsts.2014.2561
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