On order-bounded subsets of locally solid Riesz spaces

In a topological Riesz space there are two types of bounded subsets: order bounded subsets and topologically bounded subsets. It is natural to ask (1) whether an order bounded subset is topologically bounded and (2) whether a topologically bounded subset is order bounded. A classical result gives a partial answer to (1) by saying that an order bounded subset of a locally solid Riesz space is topologically bounded. This paper attempts to further investigate these two questions. In particular, we show that (i) there exists a non-locally solid topological Riesz space in which every order bounded subset is topologically bounded; (ii) if a topological Riesz space is not locally solid, an order bounded subset need not be topologically bounded; (iii) a topologically bounded subset need not be order bounded even in a locally convex-solid Riesz space. Next, we show that (iv) if a locally solid Riesz space has an order bounded topological neighborhood of zero, then every topologically bounded subset is order bounded; (v) however, a locally convex-solid Riesz space may not possess an order bounded topological neighborhood of zero even if every topologically bounded subset is order bounded; (vi) a pseudometrizable locally solid Riesz space need not have an order bounded topological neighborhood of zero. In addition, we give some results about the relationship between order bounded subsets and positive homogeneous operators

Fuzzy Riesz subspaces, fuzzy ideals, fuzzy bands and fuzzy band projections

Fuzzy ordered linear spaces, Riesz spaces, fuzzy Archimedean spaces and $\sigma$-complete fuzzy Riesz spaces were defined and studied in several works. Following the efforts along this line, we define fuzzy Riesz subspaces, fuzzy ideals, fuzzy bands and fuzzy band projections and establish their fundamental properties

Pseudoscalar or vector meson production in non-leptonic decays of heavy hadrons

We have addressed the study of non-leptonic weak decays of heavy hadrons ($\Lambda_b, \Lambda_c, B$ and $D$), with external and internal emission to give two final hadrons, taking into account the spin-angular momentum structure of the mesons and baryons produced. A detailed angular momentum formulation is developed which leads to easy final formulas. By means of them we have made predictions for a large amount of reactions, up to a global factor, common to many of them, that we take from some particular data. Comparing the theoretical predictions with the experimental data, the agreement found is quite good in general and the discrepancies should give valuable information on intrinsic form factors, independent of the spin structure studied here. The formulas obtained are also useful in order to evaluate meson-meson or meson-baryon loops, for instance of $B$ decays, in which one has PP, PV, VP or VV intermediate states, with P for pseudoscalar mesons and V for vector meson and lay the grounds for studies of decays into three final particles.Comment: 54 pages, 7 figures, 13 tables; v2: 60 pages, 9 figures, 14 tables, discussion added, references added, version to appear in Eur.Phys.J.