Multipliers for p-Bessel sequences in Banach spaces

Multipliers have been recently introduced as operators for Bessel sequences and frames in Hilbert spaces. These operators are defined by a fixed multiplication pattern (the symbol) which is inserted between the analysis and synthesis operators. In this paper, we will generalize the concept of Bessel multipliers for p-Bessel and p-Riesz sequences in Banach spaces. It will be shown that bounded symbols lead to bounded operators. Symbols converging to zero induce compact operators. Furthermore, we will give sufficient conditions for multipliers to be nuclear operators. Finally, we will show the continuous dependency of the multipliers on their parameters.Comment: 17 page

Viable models with non-universal gaugino mediated supersymmetry breaking

Recently, extra dimensional SUSY GUT models have been proposed in which compactification of the extra dimension(s) leads to a breakdown of the gauge symmetry and/or supersymmetry. We examine a particular class of higher-dimensional models exhibiting supersymmetry and SU(5) or SO(10) GUT symmetry. SUSY breaking occurs on a hidden brane, and is communicated to the visible brane via gaugino mediation. Non-universal gaugino masses are developed at the compactification scale as a consequence of a restricted gauge symmetry on the hidden brane. In this case, the compactification scale is at or slightly below the GUT scale. We examine the parameter space of such models where gaugino masses are related due to a Pati-Salam symmetry on the hidden brane. We find limited but significant regions of model parameter space where a viable spectra of SUSY matter is generated. Our results are extended to the more general case of three independent gaugino masses; here we find that large parameter space regions open up for large values of the U(1) gaugino mass M_1. We also find the relic density of neutralinos for these models to be generally below expectations from cosmological observations, thus leaving room for hidden sector states to make up the bulk of cold dark matter. Finally, we evaluate the branching fraction BF(b -> s gamma) and muon anomalous magnetic moment a_\mu.Comment: 21 pages, 9 figure