Structure of quasi ordered ∗-vector spaces | ||
| Iranian Journal of Science | ||
| مقاله 7، دوره 38، شماره 4، اسفند 2014، صفحه 445-453 اصل مقاله (482.37 K) | ||
| نوع مقاله: Regular Paper | ||
| شناسه دیجیتال (DOI): 10.22099/ijsts.2014.2561 | ||
| نویسندگان | ||
| G. H. Esslamzadeh* ؛ M. Moazami Goodarzi؛ F. Taleghani | ||
| Department of Mathematics, College of Sciences, Shiraz University, Shiraz 71454, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Quasi ordered ∗-vector space؛ bounded algebra؛ quasi operator system؛ Archimedeanization | ||
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آمار تعداد مشاهده مقاله: 3,858 تعداد دریافت فایل اصل مقاله: 2,309 |
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