The Ordered Vector Space Structure of Jc-Algebras†

1971 ◽  
Vol s3-22 (2) ◽  
pp. 359-368
Author(s):  
John W. Bunce
Keyword(s):  
Vector Space ◽  
Space Structure ◽  
Ordered Vector Space

scholarly journals FINITE-DIMENSIONAL ORDERED VECTOR SPACES WITH RIESZ INTERPOLATION AND EFFROS–SHEN’S UNIMODULARITY CONJECTURE

2016 ◽  
Vol 101 (2) ◽  
pp. 277-287
Author(s):  
AARON TIKUISIS
Keyword(s):  
Vector Space ◽  
Inductive Limit ◽  
Space Structure ◽  
Vector Spaces ◽  
Ordered Vector Space ◽  
Finite Dimensional ◽  
Ordered Vector Spaces

It is shown that, for any field $\mathbb{F}\subseteq \mathbb{R}$, any ordered vector space structure of $\mathbb{F}^{n}$ with Riesz interpolation is given by an inductive limit of a sequence with finite stages $(\mathbb{F}^{n},\mathbb{F}_{\geq 0}^{n})$ (where $n$ does not change). This relates to a conjecture of Effros and Shen, since disproven, which is given by the same statement, except with $\mathbb{F}$ replaced by the integers, $\mathbb{Z}$. Indeed, it shows that although Effros and Shen’s conjecture is false, it is true after tensoring with $\mathbb{Q}$.

scholarly journals FOCK SPACE STRUCTURE FOR THE SIMPLEST PARASUPERSYMMETRIC SYSTEM

2001 ◽  
Vol 16 (15) ◽  
pp. 963-971 ◽  
Author(s):  
WEIMIN YANG ◽  
SICONG JING
Keyword(s):  
Vector Space ◽  
State Vector ◽  
Fock Space ◽  
Space Structure ◽  
The State ◽  
Degree Of Freedom ◽  
Basis Vectors

Structure of the state-vector space for a system consisting of one mode para-Bose and one mode para-Fermi degree of freedom with the same parastatistics order p is studied and a complete, orthonormal set of basis vectors in this space is constructed. There is an intrinsic double degeneracy for state vectors with m parabosons and n parafermions, where m ≠ 0, n ≠ 0 and n ≠ p. It is also shown that the degeneracy plays a key role in realization of exact supersymmetry for such a system.

The learning of the vector space structure by sixth grade students

1971 ◽  
Vol 4 (2) ◽  
pp. 166-181 ◽  
Author(s):  
William E. Lamon ◽  
Leslie E. Huber
Keyword(s):  
Vector Space ◽  
Sixth Grade ◽  
Space Structure ◽  
Sixth Grade Students

The order-bound topology

1972 ◽  
Vol 71 (2) ◽  
pp. 321-327 ◽  
Author(s):  
Yau-Chuen Wong
Keyword(s):  
Vector Space ◽  
Positive Cone ◽  
Order Topology ◽  
Bounded Subset ◽  
Partially Ordered ◽  
Convex Topology ◽  
Ordered Vector Space ◽  
Partially Ordered Vector Space ◽  
Locally Convex Topology ◽  
Locally Convex

Let (E, C) be a partially ordered vector space with positive cone C. The order-bound topology Pb(6) (order topology in the terminology of Schaefer(9)) on E is the finest locally convex topology for which every order-bounded subset of E is topologically bounded.

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