Hahn's Embedding Theorem for orders and harmonic analysis on groups with ordered duals

The Hahn Embedding Theorem for Abelian Lattice-ordered Groups

An embedding theorem for Eichler orders

Let B be a quaternion algebra over number field K : Assume that B satisfies the Eichler condition (i.e., there is at least one archimedean place which is unramified in B). Let O be an order in a quadratic extension L of K: The Eichler orders of B which admit an embedding of O are determined. This is a generalization of Chinburg and Friedman’s embedding theorem for maximal orders. r 2004 Elsevie...

A Correction and Improvement of a Theorem on Ordered Groups

5. I. Kaplansky, Projections in Banach algebras, Ann. of Math. vol. 53 (1951) pp. 235-249. 6. -, Rings of operators, University of Chicago mimeographed notes, 1955. 7. L. H. Loomis, An introduction to abstract harmonic analysis, D. van Nostrand, 1953. 8. T. Ogasawara and K. Yoshinaga, Extension of ^-application to unbounded operators, J. Sci. Hiroshima Univ. Ser. A. vol. 19 (1955) pp. 273-299. ...

On intermediate value theorem in ordered Banach spaces for noncompact and discontinuous mappings

In this paper, a vector version of the intermediate value theorem is established. The main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{On fixed point theorems for monotone increasing vector valued mappings via scalarizing}, Positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...

A monotonicity theorem for dp-minimal densely ordered groups

Dp-minimality is a common generalization of weak minimality and weak o-minimality. If T is a weakly o-minimal theory then it is dp-minimal (Fact 2.2), but there are dp-minimal densely ordered groups that are not weakly o-minimal. We introduce the even more general notion of inpminimality and prove that in an inp-minimal densely ordered group, every definable unary function is a union of finitel...