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.

Seeking the New Normal? Troubled Spaces of Encountering Visible Differences in Warsaw

In times of globalisation and super-mobility, ideas of normality are in turmoil. In different societies in, across and beyond Europe, we face the challenge of undoing specific notions of normality and creating more inclusive societies with an open culture of learning to live with differences. The scope of
the paper is to introduce some findings on encounters with difference and negotiations of social values in relation to a growing visibility of difference after 1989 in Poland, on the background of a critique of normality/normalisation and normalcy.On the basis of interviews conducted inWarsaw, we investigate how normality/normalisation discourses of visible homosexuality and physical disability are incorporated into individual self-reflections and justifications of prejudices (homophobia and disabilism). More specifically we argue that there are moments of ‘cultural transgressions’ present in everyday practices towards ‘visible’sexual and (dis)ability difference.

'Dancing the Downward Slide: Spaces of Affective Adjacency in Rian and Bird with Boy'

This chapter examines how the choreography of affect in two dance theatre works creates a space of affective adjacency—a space in which the building of an alternative structure of feeling and an alternative economy of the body can be experienced. Focusing on the choreographic use of repetition in Junk Ensemble’s Bird With Boy (2011) and Fabulous Beast Dance Theatre’s Rian (2011), it shows how the work required to build an alternative affective space can become visible. Although affect is most often viewed as a preconscious, ephemeral phenomenon (a passage of intensities), that can have little or no lasting impact on socio-political action, theorists such as Megan Watkins have argued for a consideration of the ‘cumulative aspects of affect’. Highlighting Spinoza’s distinction between affectus (the capacity for a body to affect and be affected), and affectio (the impact the affecting body leaves on the affected), Watkins points out that affectio can ‘leave a residue’ allowing for the ‘capacity of affect to be retained, to accumulate, to form dispositions and thus shape subjectivities’. The choreography of repetition in Bird With Boy and Rian presents sites for an examination of this accumulation of affect and its capacity not only to form and shape dispositions, but also, as Lauren Berlant suggests, ‘to move along and make worlds, situations, and environments’.

Technology and the architecture of markets: re-configuring the Canadian equity market

This paper examines the relation between technical possibilities, liberal logics, and the concrete reconfiguration of markets. It focuses on the enrolling of innovations in communication and information technologies into the markets traditionally dominated by stock exchanges. With the development of capacities to trade on-screen, the power of incumbent market makers has been challenged as a less stable array of competing quasi-public and private marketplaces emerges. Developing a case study of the Toronto Stock Exchange, I argue that narrative emphasis on the performative power of sociotechnical innovations, the deterritorialisation of financial relations, and the erosion of state capacities needs qualification. A case is made for the importance of developing an understanding of: the spaces of encounter between emerging social technologies and property rights, rules of exchange, and structures of governance; and the interplay of orderings of different institutional composition and spatial reach in the reconfiguration of market architectures. Only then can a better grasp be gained of the evolving dynamics between making markets, the regulatory powers of the state, and their delimitations.

The spatial turn: geographical approaches in the history of science

Over the past decade or so a number of historians of science and historical geographers, alert to the situated nature of scientific knowledge production and reception and to the migratory patterns of science on the move, have called for more explicit treatment of the geographies of past scientific knowledge. Closely linked to work in the sociology of scientific knowledge and science studies and connected with a heightened interest in spatiality evident across the humanities and social sciences this ‹spatial turn’ has informed a wide-ranging body of work on the history of science. This discussion essay revisits some of the theoretical props supporting this turn to space and provides a number of worked examples from the history of the life sciences that demonstrate the different ways in which the spaces of science have been comprehended.

Analyticity of smooth eigenfunctions and spectral analysis of the Gauss map

We provide a sufficient condition of analyticity of infinitely differentiable eigenfunctions of operators of the form Uf(x) = integral a(x, y) f(b( x, y)) mu(dy) acting on functions f: [u, v] --> C ( evolution operators of one-dimensional dynamical systems and Markov processes have this form). We estimate from below the region of analyticity of the eigenfunctions and apply these results for studying the spectral properties of the Frobenius-Perron operator of the continuous fraction Gauss map. We prove that any infinitely differentiable eigenfunction f of this Frobenius-Perron operator, corresponding to a non-zero eigenvalue admits a (unique) analytic extension to the set C\(-infinity, 1]. Analyzing the spectrum of the Frobenius Perron operator in spaces of smooth functions, we extend significantly the domain of validity of the Mayer and Ropstorff asymptotic formula for the decay of correlations of the Gauss map.