Shift invariant preduals of ℓ₁(ℤ)

The Banach space ℓ<sub>1</sub>(ℤ) admits many non-isomorphic preduals, for example, C(K) for any compact countable space K, along with many more exotic Banach spaces. In this paper, we impose an extra condition: the predual must make the bilateral shift on ℓ<sub>1</sub>(ℤ) weak<sup>*</sup>-continuous. This is equivalent to making the natural convolution multiplication on ℓ<sub>1</sub>(ℤ) separately weak*-continuous and so turning ℓ<sub>1</sub>(ℤ) into a dual Banach algebra. We call such preduals <i>shift-invariant</i>. It is known that the only shift-invariant predual arising from the standard duality between C<sub>0</sub>(K) (for countable locally compact K) and ℓ<sub>1</sub>(ℤ) is c<sub>0</sub>(ℤ). We provide an explicit construction of an uncountable family of distinct preduals which do make the bilateral shift weak<sup>*</sup>-continuous. Using Szlenk index arguments, we show that merely as Banach spaces, these are all isomorphic to c<sub>0</sub>. We then build some theory to study such preduals, showing that they arise from certain semigroup compactifications of ℤ. This allows us to produce a large number of other examples, including non-isometric preduals, and preduals which are not Banach space isomorphic to c<sub>0</sub>

Completely positive multipliers of quantum groups

We show that any completely positive multiplier of the convolution algebra of the dual of an operator algebraic quantum group \G (either a locally compact quantum group, or a quantum group coming from a modular or manageable multiplicative unitary) is induced in a canonical fashion by a unitary corepresentation of \G. It follows that there is an order bijection between the completely positive multipliers of L^1(\G) and the positive functionals on the universal quantum group C_0^u(\G). We provide a direct link between the Junge, Neufang, Ruan representation result and the representing element of a multiplier, and use this to show that their representation map is always weak$^*$-weak$^*$-continuous.Comment: 18 pages; major rewrit

Closed quantum subgroups of locally compact quantum groups

We investigate the fundamental concept of a closed quantum subgroup of a locally compact quantum group. Two definitions - one due to S.Vaes and one due to S.L.Woronowicz - are analyzed and relations between them discussed. Among many reformulations we prove that the former definition can be phrased in terms of quasi-equivalence of representations of quantum groups while the latter can be related to an old definition of Podle\'s from the theory of compact quantum groups. The cases of classical groups, duals of classical groups, compact and discrete quantum groups are singled out and equivalence of the two definitions is proved in the relevant context. A deep relationship with the quantum group generalization of Herz restriction theorem from classical harmonic analysis is also established, in particular, in the course of our analysis we give a new proof of Herz restriction theorem.Comment: 24 pages, v3 adds another reference. The paper will appear in Advances in Mathematic

Phosphorus supply affects seedling growth of mycorrhizal but not cluster-root forming jarrah-forest species

Aims Fertiliser is often used to kick-start ecological restoration despite growing evidence of the potentially negative impacts on plant diversity. Jarrah (Eucalyptus marginata) forest species growing on nutrient (especially phosphorus) impoverished soils in southwestern Australia have a suite of adaptations for phosphorus (P) acquisition, including the formation of cluster roots, and associations with mycorrhizal fungi. Here we investigated how escalating P supply, along with a stoichiometric adjustment of nitrogen (N) supply, impacted the growth and nutrition of a wide range of jarrah forest seedlings. Methods In a pot experiment, we measured seedling biomass and nutritional responses of 12 jarrah forest species to a gradient of P supply in relation to N supply, and for the mycorrhizal species, inoculation with arbuscular mycorrhizal fungi. Results Three cluster-root forming species did not respond to increasing P, probably because they were reliant on seed P. Generally, mycorrhizal species showed a positive biomass response to increasing P when N was available. Mycorrhizas benefited seedling growth at low P (9 mg P added per kg of jarrah forest soil) when N was also available, and were parasitic to seedling growth at high P (243 mg P/ kg soil) without additional N. Conclusions These results highlight importance of P and N supply in determining the nature of the symbiosis between plants and mycorrhizal fungi. Since P supply has the potential to reduce plant growth, for a range of species, our results suggest careful consideration of fertiliser amounts for ecological restoration of ecosystems adapted to nutrient poor soils

The determinants of election to the United Nations Security Council

This is the author's accepted manuscript. The final publication is available at Springer via http://dx.doi.org/10.1007/s11127-013-0096-4.The United Nations Security Council (UNSC) is the foremost international body responsible for the maintenance of international peace and security. Members vote on issues of global importance and consequently receive perks—election to the UNSC predicts, for instance, World Bank and IMF loans. But who gets elected to the UNSC? Addressing this question empirically is not straightforward as it requires a model that allows for discrete choices at the regional and international levels; the former nominates candidates while the latter ratifies them. Using an original multiple discrete choice model to analyze a dataset of 180 elections from 1970 to 2005, we find that UNSC election appears to derive from a compromise between the demands of populous countries to win election more frequently and a norm of giving each country its turn. We also find evidence that richer countries from the developing world win election more often, while involvement in warfare lowers election probability. By contrast, development aid does not predict election

Equitable representation in councils: theory and an application to the United Nations Security Council

We analyze democratic equity in council voting games (CVGs). In a CVG, a voting body containing all members delegates decision-making to a (time-varying) subset of its members, as describes, e.g., the relationship between the United Nations General Assembly and the United Nations Security Council (UNSC). We develop a theoretical framework for analyzing democratic equitability in CVGs at both the country and region levels, and for different assumptions regarding preference correlation. We apply the framework to evaluate the equitability of the UNSC, and the claims of those who seek to reform it. We find that the individual permanent members are overrepresented by between 21.3 times (United Kingdom) and 3.8 times (China) from a country-level perspective, while from a region perspective Eastern Europe is the most heavily overrepresented region with more than twice its equitable representation, and Africa the most heavily underrepresented. Our equity measures do not preclude some UNSC members from exercising veto rights, however

Weakly almost periodic functionals on the measure algebra

It is shown that the collection of weakly almost periodic functionals on the convolution algebra of a commutative Hopf von Neumann algebra is a C*-algebra. This implies that the weakly almost periodic functionals on M(G), the measure algebra of a locally compact group G, is a C*-subalgebra of M(G)* = C(G)**. The proof builds upon a factorisation result, due to Young and Kaiser, for weakly compact module maps. The main technique is to adapt some of the theory of corepresentations to the setting of general reflexive Banach spaces

Data from: Long-term data suggest jarrah-forest establishment at restored mine sites is resistant to climate variability

1. Global climate change is projected to increase the frequency and intensity of drought in dry regions due to warming temperatures and declining rainfall. Severe drought can trigger tree mortality and drive persistent vegetation change. 2. To date, most empirical studies have focused on drought-induced mortality of adult trees, but this needs to be matched by similar efforts to understand drought impacts on seedling establishment if we are to understand the resilience of the world's forests to projected climate change. 3. The Eucalyptus marginata (jarrah)-forest ecoregion of south-western Australia has experienced a 17% reduction in mean annual rainfall from 1975 to 2011 compared with mean rainfall from 1900 to 1974. Drought-induced mortality of adult trees has been documented for jarrah forest, but there is limited understanding of its capacity to recover, making it difficult to predict the likelihood of persistent effects. 4. Long-term records of jarrah-forest restoration following bauxite mining are available for the 19-year period between 1992 and 2010. Records include annual data on seedling establishment in restored mine sites for 587 species in 1938 plots during a period of climatic variability. 5. We built a structural equation model to discriminate the relative effects of climate, restoration practice, and their interactive effects on three response variables including species richness of the restored plant assemblages. Climate variability had a significant negative effect on richness, but the effect size was relatively small, being less than half that of varying restoration practice. We suggest this is due, in part, to the reliability of rainfall (i.e. no change in the coefficient of variation, seasonality or evenness, between recent and historical climates) despite a threefold difference in the absolute amount of wet-season rainfall. Importantly, there was no evidence that restoration practices were compromised by interacting effects of increased climate variability. 6. Synthesis. Jarrah-forest establishment in a restoration context appears resistant to recent changes in climate. Our research highlights the importance of deriving multiple metrics of climate change to understand community responses. In particular, rainfall reliability should be a focus of future research to determine its broader significance to seedling establishment in forests subject to a drying climate