On strongly reflexive topological groups

Let Gˆ denote the Pontryagin dual of an abelian topological group G. Then G is reflexive if it is topologically isomorphic to Gˆˆ, strongly reflexive if every closed subgroup and every Hausdorff quotient of G and of Gˆ is reflexive. It is well known that locally compact abelian (LCA) groups are strongly reflexive. W. Banaszczyk [Colloq. Math. 59 (1990), no. 1, 53–57], extending an earlier result of R. Brown, P. J. Higgins and S. A. Morris [Math. Proc. Cambridge Philos. Soc. 78 (1975), 19–32], showed that all countable products and sums of LCA groups are strongly reflexive. L. Aussenhofer [Dissertationes Math. (Rozprawy Mat.) 384 (1999), 113 pp.] showed that all Čech-complete nuclear groups are strongly reflexive. It is an open question whether the strongly reflexive groups are exactly the Čech-complete nuclear groups and their duals. A Hausdorff topological group G is almost metrizable if and only if it has a compact subgroup K such that G/K is metrizable [W. Roelcke and S. Dierolf, Uniform structures on topological groups and their quotients, McGraw-Hill, New York, 1981]. In this paper it is shown that the annihilator of a closed subgroup of an almost metrizable group G is topologically isomorphic to the dual of the corresponding Hausdorff quotient, and an analogous statement holds for the character group of G. It then follows that an almost metrizable group is strongly reflexive only if its Hausdorff quotients and those of its dual are reflexive

Pontryagin reflexive groups are not determined by their continuous characters

A theorem of Glicksberg states that, for an abelian group G, two locally compact topologies with the same set of continuous characters must coincide. In [12] it is asserted that this fact also holds for two Pontryagin reflexive topologies. We prove here that this statement is not correct, and we give some additional conditions under which it is true. We provide some examples of classes of groups determined by their continuous characters

Strong Reflexivity of Abelian Groups

A reflexive topological group G is called strongly reflexive if each closed subgroup and each Hausdorff quotient of the group G and of itsdua l group isre flexive. In this paper we establish an adequate concept of strong reflexivity for convergence groups. We prove that complete metrizable nuclear groups and products of countably many locally compact topological groupsare BB-strongly reflexive

The Pontryagin duality of sequential limits of topological Abelian groups

We prove that direct and inverse limits of sequences of reflexive Abelian groups that are metrizable or k -spaces, but not necessarily locally compact, are reflexive and dual of each other provided some extra conditions are satisfied by the sequences

An approach to duality on abelian precompact groups

We prove that every dense Subgroup of a topological abelian group has the same 'convergence dual' as the whole group. By the 'convergence dual' we mean the character group endowed with the continuous convergence structure. We draw as a corollary that the continuous convergence Structure on the character group Of a precompact group is discrete and therefore a non-compact precompact group Is never reflexive in the sense of convergence. We do not know if the same statement holds also for reflexivity in the sense of Pontryagin; at least M the category of metrizable abelian groups it does

On g-barrelled groups and their permanence properties

The g-barrelled groups constitute a vast class of abelian topological groups. It might be considered as a natural extension of the class of barrelled topological vector spaces. In this paper we prove that g-barrelledness is a multiplicative property, thus we obtain new examples of g-barrelled groups. We also prove that direct sums and inductive limits of g-barrelled locally quasi-convex groups are g-barrelled, too. Other permanence properties are considered as well

On Schwartz Groups

In this paper we introduce a notion of a Schwartz group, which turns out to be coherent with the well known concept of a Schwartz topo- logical vector space. We establish several basic properties of Schwartz groups and show that free topological Abelian groups, as well as free locally convex spaces, over a hemicompact k{space are Schwartz groups. We also prove that every hemicompact k{space topological group, in particular the Pontryagin dual of a metrizable topological group, is a Schwartz group

Search for a W' boson decaying to a bottom quark and a top quark in pp collisions at sqrt(s) = 7 TeV

Results are presented from a search for a W' boson using a dataset corresponding to 5.0 inverse femtobarns of integrated luminosity collected during 2011 by the CMS experiment at the LHC in pp collisions at sqrt(s)=7 TeV. The W' boson is modeled as a heavy W boson, but different scenarios for the couplings to fermions are considered, involving both left-handed and right-handed chiral projections of the fermions, as well as an arbitrary mixture of the two. The search is performed in the decay channel W' to t b, leading to a final state signature with a single lepton (e, mu), missing transverse energy, and jets, at least one of which is tagged as a b-jet. A W' boson that couples to fermions with the same coupling constant as the W, but to the right-handed rather than left-handed chiral projections, is excluded for masses below 1.85 TeV at the 95% confidence level. For the first time using LHC data, constraints on the W' gauge coupling for a set of left- and right-handed coupling combinations have been placed. These results represent a significant improvement over previously published limits.Comment: Submitted to Physics Letters B. Replaced with version publishe

Search for the standard model Higgs boson decaying into two photons in pp collisions at sqrt(s)=7 TeV

A search for a Higgs boson decaying into two photons is described. The analysis is performed using a dataset recorded by the CMS experiment at the LHC from pp collisions at a centre-of-mass energy of 7 TeV, which corresponds to an integrated luminosity of 4.8 inverse femtobarns. Limits are set on the cross section of the standard model Higgs boson decaying to two photons. The expected exclusion limit at 95% confidence level is between 1.4 and 2.4 times the standard model cross section in the mass range between 110 and 150 GeV. The analysis of the data excludes, at 95% confidence level, the standard model Higgs boson decaying into two photons in the mass range 128 to 132 GeV. The largest excess of events above the expected standard model background is observed for a Higgs boson mass hypothesis of 124 GeV with a local significance of 3.1 sigma. The global significance of observing an excess with a local significance greater than 3.1 sigma anywhere in the search range 110-150 GeV is estimated to be 1.8 sigma. More data are required to ascertain the origin of this excess.Comment: Submitted to Physics Letters