DISCRETE VECTOR LATTICES AND THE RANGE OF ORTHOMORPHISMS

作者：Boulabiar K^*; Buskes G

来源：Journal of Algebra and Its Applications, 2013, 12(1): 1250136.

DOI：10.1142/S0219498812501368

• Discrete vector lattice
• orthomorphism
• weak topology
• order ideal
• uniform completion

We give a counterexample to Theorem 3.2 in Toumi and Toumi [The range of an orthomorphism, J. Algebra Appl. 8 (2009) 863-868]. In the process we add a new equivalent statement to those in Theorem 7.48 of Aliprantis and Burkinshaw [Locally Solid Riesz Spaces with Applications to Economics, Mathematical Surveys and Monographs, Vol. 105 (American Mathematical Society, 2003)].

• 出版日期2013-2