Rota’s universal operators and invariant subspaces in Hilbert spaces

A Hilbert space operator is called universal (in the sense of Rota) if every operator on the Hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces. We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a quasi-nilpotent injective compact operator with dense range. In articular, this new universal operator invites an approach to the Invariant Subspace Problem that uses properties of operators that commute with the universal operator.

Care-less spaces and identity construction:transition to secondary school for disabled children

There is a growing body of literature which marks out a feminist ethics of care and it is within this framework we understand transitions from primary to secondary school education can be challenging and care-less, especially for disabled children. By exploring the narratives of parents and professionals, we investigate transitions and self-identity, as a meaningful transition depends on the care-full spaces pupils inhabit. These education narratives are all in the context of privileging academic attainment and a culture of testing and examinations. Parents and professionals, as well as children are also surveyed. Until there are care-full education processes, marginalisation will remain, impacting on disabled children’s transition to secondary school and healthy identity construction. Moreover, if educational challenges are not addressed, their life chances are increasingly limited. Interdependent caring work enables engagement in a meaningful education and positive identity formation. In school and at home, care-full spaces are key in this process.

"I’m complicit and I’m ambivalent and that’s crazy":care-less spaces for women in the academy

This paper is about three working class women academics in their 40s, who are at different phases in their career. I take a reflexive, feminist, (Reay 2000, 2004, Ribbens and Edwards 1998) life story approach (Plummer, 2001) in order to understand their particular narratives about identity, complicity, relationships and discomfort within the academy, and then how they inhabit care-less spaces. However unique their narratives, I am able to explore an aspect of higher education – women and their working relationships – through a lens of care-less spaces, and argue that care-less-ness in the academy, can create and reproduce animosity and collusion. Notably, this is damaging for intellectual pursuits, knowledge production and markedly, the identity of woman academics. In introducing this work, I first contextualise women in the academy and define the term care-less spaces, then move onto discuss feminist methods. I then explore and critique in some detail, the substantive findings under the headings of ‘complicity and ‘faking’ it’ and ‘publishing and collaboration’. The final section concludes the paper by drawing on Herring’s (2013) legal premise, in the context of care ethics, as a way to interrogate particular care-less spaces within higher education.

Spaces of Order: An African Poetics of Space

“Spaces of Order” argues that the African novel should be studied as a revolutionary form characterized by aesthetic innovations that are not comprehensible in terms of the novel’s European archive of forms. It does this by mapping an African spatial order that undermines the spatial problematic at the formal and ideological core of the novel—the split between a private, subjective interior, and an abstract, impersonal outside. The project opens with an examination of spatial fragmentation as figured in the “endless forest” of Amos Tutuola’s The Palmwine Drinkard (1952). The second chapter studies Chinua Achebe’s Things Fall Apart (1958) as a fictional world built around a peculiar category of space, the “evil forest,” which constitutes an African principle of order and modality of power. Chapter three returns to Tutuola via Ben Okri’s The Famished Road (1991) and shows how the dispersal of fragmentary spaces of exclusion and terror within the colonial African city helps us conceive of political imaginaries outside the nation and other forms of liberal political communities. The fourth chapter shows Nnedi Okorafor—in her 2014 science-fiction novel Lagoon—rewriting Things Fall Apart as an alien-encounter narrative in which Africa is center-stage of a planetary, multi-species drama. Spaces of Order is a study of the African novel as a new logic of world making altogether.

Analytic Torsion, the Eta Invariant, and Closed Differential Forms on Spaces of Metrics

The central idea of this dissertation is to interpret certain invariants constructed from Laplace spectral data on a compact Riemannian manifold as regularized integrals of closed differential forms on the space of Riemannian metrics, or more generally on a space of metrics on a vector bundle. We apply this idea to both the Ray-Singer analytic torsion

and the eta invariant, explaining their dependence on the metric used to define them with a Stokes' theorem argument. We also introduce analytic multi-torsion, a generalization of analytic torsion, in the context of certain manifolds with local product structure; we prove that it is metric independent in a suitable sense.

Governmentality and exclusion in post-disaster spaces : conducting the conduct of the survivors of Typhoon Sendong in Cagayan de Oro, Philippines

Lorsque les aléas naturels se déroulent en catastrophes, les réponses des religieux, de l’Etat, et d’autres acteurs puissants dans une société révèlent à la fois les relations complexes entre ces parties et leur pouvoir dans la production des espaces auxquelles les survivants accèdent. La réponse en cas de catastrophe comprend la création d’espaces post-catastrophes, tels que des centres d’évacuation, des logements de transition et des sites de réinstallation permanente, qui ciblent spécifiquement un sous-ensemble particulier de survivants, et visent à les aider à survivre, à faire face, et à se remettre de la catastrophe. Les acteurs puissants dans une société dirigent les processus de secours, de récupération et de reconstruction sont des acteurs puissants qui cherchent à problématiser et à rendre un problème technique dans des termes qu’ils sont idéalement placés pour aborder à travers une variété d'interventions. Ce projet de recherche vise à répondre à la question: où les survivants d'une catastrophe reconstruisent-ils leurs vies et leurs moyens de subsistance? Il enquête sur un cas spécifique de la migration environnementale dans laquelle des dizaines de milliers d'habitants ont été déplacés de façon permanente et temporaire de leurs résidences habituelles après le typhon Sendong à Cagayan de Oro, Philippines en 2011. La recherche est basée sur des entretiens avec les acteurs puissants et les survivants, des vidéos participatives réalisées par des survivants pauvres urbains, et des activités de cartographie. L’étude se fonde sur la théorie féministe, les études de migration, les études dans la gouvernementalité, la recherche sur les changements de l’environnement planétaire, et les études régionales afin de situer les diverses expériences de la migration dans un contexte géographique et historique. Cette thèse propose une topographie critique dans laquelle les processus et les pratiques de production d’espaces post-catastrophe sont exposés. Parce que l’espace est nécessairement malléable, fluide, et relationnelle en raison de l'évolution constante des activités, des conflits, et des expériences qui se déroulent dans le paysage, une analyse de l'espace doit être formulée en termes de relations sociales qui se produisent dans et au-delà de ses frontières poreuses. En conséquence, cette étude explore comment les relations sociales entre les survivants et les acteurs puissants sont liées à l’exclusion, la gouvernementalité, la mobilité, et la production des espaces, des lieux et des territoires. Il constate que, si les trajectoires de migration de la plupart des survivants ont été confinés à l'intérieur des limites de la ville, les expériences de ces survivants et leur utilisation des espaces urbains sont très différentes. Ces différences peuvent être expliquées par des structures politiques, économiques, et sociales, et par les différences religieuses, économiques, et de genre. En outre, il fait valoir que les espaces post-catastrophe doivent être considérés comme des «espaces d’exclusion» où les fiduciaires exercent une rationalité gouvernementale. C’est-à-dire, les espaces post-catastrophe prétendument inclusives servent à marginaliser davantage les populations vulnérables. Ces espaces offrent aussi des occasions pour les acteurs puissants dans la société philippine d'effectuer des interventions gouvernementales dans lesquelles certaines personnes et les paysages sont simplifiées, rendues lisibles, et améliorés.

Spaces of Visibility for the Migrants of Lampedusa: The Counter Narrative of the Aesthetic Discourse

Political, legal, and media discourse around ‘boat-migrants’ arriving in Lampedusa share a tendency to focus on an unnamed and anonymous mass of people in order to build and sustain a Border Spectacle revolving around immigration to Italy. In this context, where very little space is usually left to individual migrant voices, this article challenges this common understanding of immigration to Lampedusa by showing a different side of the story, a story told by the real actors of the Mediterranean passage, the migrants themselves, who, by relying on the realm of aesthetics, have managed to gain visibility and to become ‘subjects of power.’

Nagaland: Borders, Boundaries, Belonging: Contested spaces and disputed narratives

In 2011 I travelled to three of the ‘Seven Sister’ states of old Assam, Nagaland, Meghalaya & Assam. My journey to this remote and politically sensitive region, bordering Chinese occupied Tibet, Bangladesh and Myanmar was prompted by my father’s experiences in the region during WW2 in the Burma Campaign and brought into sharp relief on-going themes in my work, the impact the past has on the present, the relationship of time and place, identity and memory and the transcultural experiences caused by war, colonisation and migration. The drawings I made on location, the objects I collected and the notes and photographs I took formed the basis of the bookwork: NAGALAND borders boundaries belonging. When making the finished work the material quality of the object and the processes by which it was made become very important. The historical resonance of the medium and the time consuming nature of the process reflect the embedding of form and idea, and paid homage to the material culture of the Naga hill tribes. The bookwork was hand-bound, handset and printed by letterpress. Some spreads were printed in 6 colours and the book took over a year to produce. I see my practice as echoing that of generations of Lady travellers; embracing the need to journey, be in a liminal space, to have a plan but not be afraid to divert from it. To be alone, take a sketchbook and make images is, for me, the definition of the itinerant illustrator; one who travels widely in geographic space, visual forms and ideas, in order to get lost and find the unlooked for.

Shared Education in contested spaces: How collaborative networks improve communities and schools

Societies which suffer from ethnic and political divisions are often characterised by patterns of social and institutional separation, and sometimes these divisions remain even after political conflict has ended. This has occurred in Northern Ireland where there is, and remains, a long-standing pattern of parallel institutions and services for the different communities. A socially significant example lies in the education system where a parallel system of Catholic and Protestant schools has been in place since the establishment of a national school system in the 1830s. During the years of political violence in Northern Ireland a variety of educational interventions were implemented to promote reconciliation, but most of them failed to create any systemic change. This paper describes a post-conflict educational initiative known as Shared Education which aims to promote social cohesion and school improvement by encouraging sustained and regular shared learning between students and broader collaboration between teachers and school leaders from different schools. The paper examines the background to work on Shared Education, describes a ‘sharing continuum’ which emerged as an evaluation and policy tool from this work and considers evidence from a case study of a Shared Education school partnership in a divided city in Northern Ireland. The paper will conclude by highlighting some of the significant social and policy impact of the Shared Education work.

‘Ulster Says No’: Regulating the consumption of commercial sex spaces and services in Northern Ireland

Commercial forms of sex such as prostitution/sex work, strip clubs and even sex shops have been the subject of much political debate and policy regulation over the last decade or so in the UK and Ireland. These myriad forms of commercial sex and land usage have managed to survive and even thrive in the face of public outcry and regulation. Despite being part of the UK we suggest that Northern Ireland has steered its own regulatory course, whereby the consumption of commercial sexual spaces and services have been the subject of intense moral and legal oversight in ways that are not apparent in other UK regions. Nevertheless, in spite of this we also argue that the context of Northern Ireland may provide some lessons for the ways that religious values and moral reasoning can influence debates on commercial sex elsewhere.

'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’.

Orbital and strongly orbital spaces

We say that a (countably dimensional) topological vector space X is orbital if there is T∈L(X) and a vector x∈X such that X is the linear span of the orbit {Tnx:n=0,1,…}. We say that X is strongly orbital if, additionally, x can be chosen to be a hypercyclic vector for T. Of course, X can be orbital only if the algebraic dimension of X is finite or infinite countable. We characterize orbital and strongly orbital metrizable locally convex spaces. We also show that every countably dimensional metrizable locally convex space X does not have the invariant subset property. That is, there is T∈L(X) such that every non-zero x∈X is a hypercyclic vector for T. Finally, assuming the Continuum Hypothesis, we construct a complete strongly orbital locally convex space.

As a byproduct of our constructions, we determine the number of isomorphism classes in the set of dense countably dimensional subspaces of any given separable infinite dimensional Fréchet space X. For instance, in X=ℓ2×ω, there are exactly 3 pairwise non-isomorphic (as topological vector spaces) dense countably dimensional subspaces.

Fast classification in incrementally growing spaces

[EN]The classification speed of state-of-the-art classifiers such as SVM is an important aspect to be considered for emerging applications and domains such as data mining and human-computer interaction. Usually, a test-time speed increase in SVMs is achieved by somehow reducing the number of support vectors, which allows a faster evaluation of the decision function. In this paper a novel approach is described for fast classification in a PCA+SVM scenario. In the proposed approach, classification of an unseen sample is performed incrementally in increasingly larger feature spaces. As soon as the classification confidence is above a threshold the process stops and the class label is retrieved...