Geometry in preduals of spaces of 2-homogeneous polynomials on Hilbert spaces

Let H be a (real or complex) Hilbert space. Using spectral theory and properties of the Schatten–Von Neumann operators, we prove that every symmetric tensor of unit norm in HoH is an infinite absolute convex combination of points of the form xox with x in the unit sphere of the Hilbert space. We use this to obtain explicit characterizations of the smooth points of the unit ball of HoH .

Decompositions of spaces of measures

Let M be the Banach space of sigma-additive complex-valued measures on an abstract measurable space. We prove that any closed, with respect to absolute continuity norm-closed, linear subspace L of M is complemented and describe the unique complement, projection onto L along which has norm 1. Using this fact we prove a decomposition theorem, which includes the Jordan decomposition theorem, the generalized Radon-Nikodym theorem and the decomposition of measures into decaying and non-decaying components as particular cases. We also prove an analog of the Jessen-Wintner purity theorem for our decompositions.

Protest practice and (tree) cultures of conflict: understanding the spaces of ‘tree maiming’ in eighteenth- and early nineteenth-century England

Developing understandings of protest and cultures of resistance has been a central theme of the 'new' cultural geography of the 1990s and 2000s. But whilst geographers of the here and now have been highly sensitive to the importance of acts of protest which occur outside of the context of broader social movements, geographers concerned with past protests have tended to focus overwhelmingly upon either understanding the development of social movements or highly specific place-based studies. Through a focus upon the hitherto ignored practice of 'tree maiming', this paper demonstrates not only the value of examining specific protest practices in helping to better understand the complexity of conflict, but also how in periods of acute socio-economic change the evolving relationship between humans and the non-human – in this case trees – is a central discourse to the protest practices of the poor. Such attacks often involved complex cultural understandings about the ways in which trees should – and should not – be socially enrolled.

Reconfiguring spaces of conflict: Northern Ireland and the impact of European integration

The Irish border has historically been one of the most contested borders in Europe. In the context of the peace process and EU membership, co-operation between Northern Ireland and the Republic of Ireland has been encouraged, supported and normalised, although internal borders of segregation stubbornly remain. This paper offers a conceptualisation of borders in conflict cases and a theoretical account of how European integration can affect their transformation. Analysis of the Northern Ireland case shows there are ambiguities within integration that allow for a ‘rebordering’ of identities at the same time as the state border diminishes in significance.

Collaborative artistic laboratories. Transfrontier spaces of cultural production

The appearance of the open code paradigm and the demands of social movements have permeated the ways in which today’s cultural institutions are organized. This article analyzes the birth of a new critical and cooperative spatiality and how it is transforming current modes of cultural research and production. It centers on the potential for establishing the new means of cooperation that are being tested in what are defined as collaborative artistic laboratories. These are hybrid spaces of research and creation based on networked and cooperative structures producing a new societal-technical body that forces us to reconsider the traditional organic conditions of the productive scenarios of knowledge and artistic practice.

Infinite Dimensional Banach spaces of functions with nonlinear properties

The aim of this paper is to show that there exist infinite dimensional Banach spaces of functions that, except for 0, satisfy properties that apparently should be destroyed by the linear combination of two of them. Three of these spaces are: a Banach space of differentiable functions on Rn failing the Denjoy-Clarkson property; a Banach space of non Riemann integrable bounded functions, but with antiderivative at each point of an interval; a Banach space of infinitely differentiable functions that vanish at infinity and are not the Fourier transform of any Lebesgue integrable function.

The spaces of knowledge: Contributions towards a historical geography of science

Reprinted in Trevor Barnes and Derek Gregory (eds), Reading Human Geography: The Poetics and Politics of Inquiry, (London: Arnold, 1997), pp. 27-48

Limits of Dissent, Perils of Activism: Spaces of Resistance and the New Security Logic

On 26 December 2003 an Israeli activist was shot by the Israeli Army while he was participating in a demonstration organized by Anarchists Against the Wall (AAtW) in the West Bank. This was the first time Israeli Soldiers have deliberately shot live bullets at a Jewish-Israeli activist. This paper is an attempt to understand the set of conditions, the enveloping frameworks, and the new discourses that have made this event, and similar shootings that soon followed, possible. Situating the actions of AAtW within a much wider context of securitization—of identities, movements, and bodies—we examine strategies of resistance which are deployed in highly securitized public spaces. We claim that an unexpected matrix of identity in which abnormality is configured as security threat render the bodies of activists especially precarious. The paper thus provides an account of the new rationales of security technologies and tactics which increasingly govern public spaces.