On the operator space structure of Hilbert spaces

Operator spaces of Hilbertian JC∗ -triples E are considered in the light of the universal ternary ring of operators (TRO) introduced in recent work. For these operator spaces, it is shown that their triple envelope (in the sense of Hamana) is the TRO they generate, that a complete isometry between any two of them is always the restriction of a TRO isomorphism and that distinct operator space structures on a fixed E are never completely isometric. In the infinite-dimensional cases, operator space structure is shown to be characterized by severe and definite restrictions upon finite-dimensional subspaces. Injective envelopes are explicitly computed.

Driving places - Marc Augé, non-places, and the geographies of England's M1 motorway

In this article I provide a critical account of the 'placing' of England's M1 motor-way. I start by critiquing Marc Auge's anthropological writings on 'non-places' which have provided a common point of reference for academics discussing spaces of travel, consumption and exchange in the contemporary world. I argue that Auge's ethnology of supermodernity results in a rather partial account of these sites, that he overstates the novelty of contemporary experiences of these spaces, and that he fails to acknowledge the heterogeneity and materiality of the social networks bound up with the production of non-places/places. I suggest that, rather than focusing on the presences and absences associated with the polarities of place and non-place, academics should examine the multiple, partial, dynamic and relational 'placings' which arise through the diverse performances and movements associated with travel, consumption and exchange. I then trace the topologies of England's M1 motorway, examining some of the different ways in which the motorway has been assembled, performed and placed over the past 45 years.

'Operation motorway': landscapes of construction on England's M1 motorway

Recent years have seen an increasing number of academics attempt to write more process-oriented and 'nonrepresentational' accounts of landscape. Drawing upon this literature, I discuss a number of the movements, materialities, and practices entailed in constructing England's M1 motorway in the late 1950s. The performances, movements and durability of a diverse range of things-including earth-moving machines, public relations brochures, maps, helicopters, senior engineers, aggregate and labourers-are shown to be important to the construction and ordering of the motorway and spaces of the construction company in different times and spaces, with people's experiences or understandings of construction, both now and in the past, emerging through memories, talk and embodied encounters with architectures, texts and artefacts which are assembled, circulated and/or archived. Aerial perspectives assumed a prominent role in depictions of construction, while journalists and engineers frequently drew upon a military vocabulary and alluded to the military nature of the project when discussing the motorway. (c) 2005 Elsevier Ltd. All rights reserved.

Realism and politics in alienated space: Trevor Griffiths's plays of the 1970s in the television studio

The television studio play is often perceived as a somewhat compromised, problematic mode in which spatial and technological constraints inhibit the signifying and aesthetic capacity of dramatic texts. Leah Panos examines the function of the studio in the 1970s television dramas of socialist playwright Trevor Griffiths, and argues that the established verbal and visual conventions of the studio play, in its confined and ‘alienated’ space, connect with and reinforce various aspects of Griffiths's particular approach and agenda. As well as suggesting ways in which the idealist, theoretical focus of the intellectual New Left is reflexively replicated within the studio, Panos explores how the ‘intimate’ visual language of the television studio allows Griffiths to create a ‘humanized’ Marxist discourse through which he examines dialectically his dramatic characters' experiences, ideas, morality, and political objectives. Leah Panos recently completed her doctoral thesis, ‘Dramatizing New Left Contradictions: Television Texts of Ken Loach, Jim Allen, and Trevor Griffiths’, at the University of Reading and is now a Postdoctoral Researcher on the AHRC funded project, ‘Spaces of Television: Production, Site and Style’, which runs from July 2010 to March 2014.

Expectation versus provision in the management and use of urban open space

This paper discusses the implications of the shifting cultural significance of public open space in urban areas. In particular, it focuses on the increasing dysfunction between people's expectations of that space and its actual provision and management. In doing so, the paper applies Lefebvre's ideas of spatiality to the evident paradigm shift from 'public' to 'private' culture, with its associated commodification of previously public space. While developing the construct of paradigm shift, the paper recognises that the former political notions inherent in the provision of public space remain in evidence. So whereas public parks were formerly seen as spaces of confrontation between the 'rationality' of public order as the 'irrationality' of individual leisure pursuits, they are now increasingly seen, particularly 'out of hours', as the domain of the dispossessed, to be defined and policed as 'dangerous'. Where once people were welcomed into public open spaces as a means of 'educating' them in good, acceptable, leisure practices, therefore, they are now increasingly excluded, but for the same ostensible reasons. Building on survey work undertaken in Reading, Berkshire, the paper illustrates how communities can become separated from 'their' space, leaving them with the overriding impression that they have been 'short-changed' in terms of both the provision and the management of urban open space. Rather than the intimacy of local space for local people, therefore, the paper argues that parks have become externalised places, increasingly responding to commercial definitions of culture and what is 'public'. Central urban open spaces are therefore increasingly becoming sites of stratification, signification of a consumer-constructed citizenship and valorisation of public life as a legitimate element of the market surface of town and city centres.

New results and open problems on Toeplitz operators in Bergman spaces

We discuss some of the recent progress in the field of Toeplitz operators acting on Bergman spaces of the unit disk, formulate some new results, and describe a list of open problems -- concerning boundedness, compactness and Fredholm properties -- which was presented at the conference "Recent Advances in Function Related Operator Theory'' in Puerto Rico in March 2010.

Hankel operators on Fock spaces

We study Hankel operators on the weighted Fock spaces Fp. The boundedness and compactness of these operators are characterized in terms of BMO and VMO, respectively. Along the way, we also study Berezin transform and harmonic conjugates on the plane. Our results are analogous to Zhu's characterization of bounded and compact Hankel operators on Bergman spaces of the unit disk.

Universally reversible JC*-triples and operator spaces

Abstract. We prove that the vast majority of JC∗-triples satisfy the condition of universal reversibility. Our characterisation is that a JC∗-triple is universally reversible if and only if it has no triple homomorphisms onto Hilbert spaces of dimension greater than two nor onto spin factors of dimension greater than four. We establish corresponding characterisations in the cases of JW∗-triples and of TROs (regarded as JC∗-triples). We show that the distinct natural operator space structures on a universally reversible JC∗-triple E are in bijective correspondence with a distinguished class of ideals in its universal TRO, identify the Shilov boundaries of these operator spaces and prove that E has a unique natural operator space structure precisely when E contains no ideal isometric to a nonabelian TRO. We deduce some decomposition and completely contractive properties of triple homomorphisms on TROs.

A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

Death has a touch of class: society and space in Brookwood Cemetery, 1853-1903

Changes in the cultures and spaces of death during the Victorian era reveal the shifting conceptualisations and mobilisations of class in this period. Using the example of Brookwood Necropolis, established 1852 in response to the contemporary burial reform debate, the paper explores tensions within the sanitary reform movement, 1853–1903. Whilst reformist ideology grounded the cemetery's practices in a discourse of inclusion, one of the consequences of reform was to reinforce class distinctions. Combined with commercial imperatives and the modern impulse towards separation of living and dead, this aspect of reform enacted a counter-discourse of alienation. The presence of these conflicting strands in the spaces and practices of the Necropolis and their changes during the time period reflect wider urban trends.

Postmodernism, culture and feminism: the aesthetics of space and performance in Rock Follies and Rock Follies of '77

This article discusses the aesthetic and spatial representational strategies of the popular studio-based musical television drama serials Rock Follies and Rock Follies of ’77. It analyses how the texts’ themes relating to women and the entertainment industry are mediated through their postmodern ironic mode and representation of fantastic spaces. Rock Follies’ distinctive stylised aesthetic and mode of caricature are analysed with reference to the visual intentions and ‘voice’ of the writer, Howard Schuman. Through considering the programmes’ various spatial strategies, the article draws attention to the importance of visual and performance style in their postmodern discourse on culture, fantasy, gender and subjectivity. Analysis of the spaces of musical performance, characters’ domestic environments and simulated entertainment spaces reveals how a dialectic is established between the escapist imaginative pleasures of fantasy and the manipulative and exploitative practices of the culture industry. The shift from the optimism of the first series, when the LittleLadies first form, to the darker mood of the second series, in which they are increasingly divided by industry pressures, is traced through changes in the aesthetics of space and characterisation. As a space of artifice, performance and electronic visual manipulation that facilitates the texts’ reflexive representation of culture and feminised fantasy, the studio’s unique aesthetic strengths emerge through this case study.

Object-love at the Science Museum: cultural geographies of museum storerooms

The field of museum geography is taking on new significance as geographers and museum-studies scholars make sense of the spatial relations between the people, things, practices and buildings that make and remake museums. In order to strengthen this spatial interest in museums, this paper makes important connections between recent work in cultural geography and museum studies on love, materiality and the museum effect. This paper marks a departure from the preoccupation with the public spaces of museums to go behind the scenes of the Science Museum in London to explore its rarely visited, but nonetheless lively, small-to-medium-sized object storerooms at Blythe House. Incorporating field diary entries and interview extracts from two research projects based upon the museum storerooms at Blythe House, this paper brings to life the social interactions that take place between museum curators and conservators and the objects they care for. This focus on object-love enables scholars to consider anew what museums are and what they are for, the life of the museum object in the storeroom, and the emotional practices of professional curatorship and conservation. This journey into the storeroom at Blythe House makes explicit how object-love shapes museum space.

Girls talk: authorship and authenticity in the reception of Lena Dunham's Girls

By examining the discourse around Lena Dunham's HBO comedy Girls (2012– present), this article argues that the programme served as a space to think through female authorship, televisual representations and cultural tensions surrounding young womanhood. Central to this discourse was the narrative asserting Girls' and Dunham's 'authenticity', originality and universality, which sought to legitimate her gendered authorship and interest in the comedy of female intimacy within HBO' s masculine prestige channel identity. Charting three cycles of discourse surrounding the programme's debut, this article explores the paratextual framing by promotional concerns, television critics and women' s websites. It highlights how journalists and critics furthered HBO's paratextual framing of Dunham, which was later countered by the networked spaces of niche online media, which used the programme as a space to productively work through industrial and cultural tensions; particularly those surrounding female comic authorship, autobiography and intersectionality.

Transreal logical space of all propositions

Transreal numbers provide a total semantics containing classical truth values, dialetheaic, fuzzy and gap values. A paraconsistent Sheffer Stroke generalises all classical logics to a paraconsistent form. We introduce logical spaces of all possible worlds and all propositions. We operate on a proposition, in all possible worlds, at the same time. We define logical transformations, possibility and necessity relations, in proposition space, and give a criterion to determine whether a proposition is classical. We show that proofs, based on the conditional, infer gaps only from gaps and that negative and positive infinity operate as bottom and top values.

Promenades in Enlightenment Madrid: the tapestry cartoons and new social spaces

Discusses how the painters of the Royal Tapestry Factory of Santa Barbara in Madrid depicted the new social spaces of the capital in the cartoons designed to be turned into tapestries for Royal apartments. The cultural and sociological role of the 'paseo' or 'promenade' is also considered.