Ueda's peak set theorem for general von Neumann algebras

We extend Ueda's peak set theorem for subdiagonal subalgebras of tracial finite von Neumann algebras, to sigma-finite von Neumann algebras (that is, von Neumann algebras with a faithful state; which includes those on a separable Hilbert space, or with separable predual.) To achieve this extension completely new strategies had to be invented at certain key points, ultimately resulting in a more operator algebraic proof of the result. Ueda showed in the case of finite von Neumann algebras that his peak set theorem is the fountainhead of many other very elegant results, like the uniqueness of the predual of such subalgebras, a highly refined F and M Riesz type theorem, and a Gleason-Whitney theorem. The same is true in our more general setting, and indeed we obtain a quite strong variant of the last mentioned theorem. We also show that set theoretic issues dash hopes for extending the theorem to some other large general classes of von Neumann algebras, for example finite or semi-finite ones. Indeed certain cases of Ueda's peak set theorem, for a von Neumann algebra M, may be seen as `set theoretic statements' about M that require the sets to not be `too large'.Comment: Revised 2017, with a new Section 2, and other improvements. Smaller corrections 2018. To appear Trans. Amer. Math. So

Post-1500 Population Flows and the Long Run Determinants of Economic Growth and Inequity

We construct a matrix showing the share of the year 2000 population in every country that is descended from people in different source countries in the year 1500. Using this matrix, we analyze how post-1500 migration has influenced the level of GDP per capita and within-country income inequality in the world today. Indicators of early development such as early state history and the timing of transition to agriculture have much better predictive power for current GDP when one looks at the ancestors of the people who currently live in a country than when one considers the history on that country’s territory, without adjusting for migration. Measures of the ethnic or linguistic heterogeneity of a country’s current population do not predict income inequality as well as measures of the ethnic or linguistic heterogeneity of the current population’s ancestors. An even better predictor of current inequality in a country is the variance of early development history of the country’s inhabitants, with ethnic groups originating in regions having longer histories of agriculture and organized states tending to be at the upper end of a country’s income distribution. However, high within-country variance of early development also predicts higher income per capita, holding constant the average level of early development.Economic Growth; Migration; Income Inequality; State History; Linquistic Distance

‘We do it to keep him alive’: bereaved individuals’ experiences of online suicide memorials and continuing bonds

This paper presents draws on interviews with individuals who have experience of creating, maintaining and utilising Facebook sites in memory of a loved one who has died by suicide. We argue that Facebook enables the deceased to be an on-going active presence in the lives of the bereaved. We highlight the potential of the Internet (and Facebook in particular) as a new and emerging avenue for the continuation of online identities and continuing bonds. Our study offers unique insight into survivors’ experiences of engaging with the virtual presence of their deceased loved one: how mourners come and go online, how this evolves over time and how the online identity of the deceased evolves even after death. We discuss how Facebook provides new ways for people to experience and negotiate death by suicide and to memorialise the deceased, highlighting the positive impact of this for survivors’ mental health. Finally, we describe the creation of tension amongst those who manage their grief in different ways