Spin spaces and positive decomposition of linear maps on ordered Banach spaces

Spin factors and generalizations are used to revisit positive generation of B(E, F), where E and F are ordered Banach spaces. Interior points of B(E, F)+ are discussed and in many cases it is seen that positive generation of B(E, F) is controlled by spin structure in F when F is a JBW-algebra.

A generalized collectively compact operator theory with an application to integral equations on unbounded domains

In this paper a generalization of collectively compact operator theory in Banach spaces is developed. A feature of the new theory is that the operators involved are no longer required to be compact in the norm topology. Instead it is required that the image of a bounded set under the operator family is sequentially compact in a weaker topology. As an application, the theory developed is used to establish solvability results for a class of systems of second kind integral equations on unbounded domains, this class including in particular systems of Wiener-Hopf integral equations with L1 convolutions kernels

Dunford-Pettis properties, Hilbert spaces and projective tensor products

We study complete continuity properties of operators onto ℓ2 and prove several results in the Dunford–Pettis theory of JB∗-triples and their projective tensor products, culminating in characterisations of the alternative Dunford–Pettis property for where E and F are JB∗-triples.

Producing leisure spaces out of thin air: the case of the Countryside Stewardship Scheme

This paper examines the growing dysfunction between the apparently increasing significance of diverse leisure practices in the countryside and the largely unchanging official response towards them. Although there is recognition in the recent rural White Paper (DOE and MAFF, 1995) that access is essential to enjoying the countryside, the construction of this term is dubious, since paid access agreements, based on producer requirements, are favoured over any form of demand-driven freedom to roam. Using the Countryside Stewardship Scheme (CSS) as an example of the incentive structure developed to promote this policy, the paper applies Plato's simulacrum as a reading of how this process is being utilised to underpin the dominant rights associated with rural property interests. In particular, the paper makes the point that rather than representing the corollary of a market situation, as its supporters claim, the CSS involves government grant for the eclectic provision of short term licences over ground which remains unmapped as anything other than its continued agricultural use. In concluding, the paper asserts that rather than representing an increase in the availability of leisure sites in the countryside, the CSS and other schemes represent a diversion from the wider and deeper socio-cultural process of continued wealth and power redistribution.

Interpolation of Hilbert and Sobolev spaces: quantitative estimates and counterexamples

This paper provides an overview of interpolation of Banach and Hilbert spaces, with a focus on establishing when equivalence of norms is in fact equality of norms in the key results of the theory. (In brief, our conclusion for the Hilbert space case is that, with the right normalisations, all the key results hold with equality of norms.) In the final section we apply the Hilbert space results to the Sobolev spaces Hs(Ω) and tildeHs(Ω), for s in R and an open Ω in R^n. We exhibit examples in one and two dimensions of sets Ω for which these scales of Sobolev spaces are not interpolation scales. In the cases when they are interpolation scales (in particular, if Ω is Lipschitz) we exhibit examples that show that, in general, the interpolation norm does not coincide with the intrinsic Sobolev norm and, in fact, the ratio of these two norms can be arbitrarily large.

Dynamical properties of S-gap shifts and other shift spaces

We study the dynamical properties of certain shift spaces. To help study these properties we introduce two new classes of shifts, namely boundedly supermultiplicative (BSM) shifts and balanced shifts. It turns out that any almost specified shift is both BSM and balanced, and any balanced shift is BSM. However, as we will demonstrate, there are examples of shifts which are BSM but not balanced. We also study the measure theoretic properties of balanced shifts. We show that a shift space admits a Gibbs state if and only if it is balanced. Restricting ourselves to S-gap shifts, we relate certain dynamical properties of an S-gap shift to combinatorial properties from expansions in non-integer bases. This identification allows us to use the machinery from expansions in non-integer bases to give straightforward constructions of S -gap shifts with certain desirable properties. We show that for any q∈(0,1) there is an S-gap shift which has the specification property and entropy q . We also use this identification to address the question, for a given q∈(0,1), how many S-gap shifts exist with entropy q? For certain exceptional values of q there is a unique S-gap shift with this entropy.

Sufficiency of Favard's condition for a class of band-dominated operators on the axis

The purpose of this paper is to show that, for a large class of band-dominated operators on $\ell^\infty(Z,U)$, with $U$ being a complex Banach space, the injectivity of all limit operators of $A$ already implies their invertibility and the uniform boundedness of their inverses. The latter property is known to be equivalent to the invertibility at infinity of $A$, which, on the other hand, is often equivalent to the Fredholmness of $A$. As a consequence, for operators $A$ in the Wiener algebra, we can characterize the essential spectrum of $A$ on $\ell^p(Z,U)$, regardless of $p\in[1,\infty]$, as the union of point spectra of its limit operators considered as acting on $\ell^p(Z,U)$.

Silchester Roman Town Insula IX: the development of an urban property c. AD 40-50 - c. AD 250

The development of an urban property in the Roman town of Calleva Atrebatum (Silchester, Hampshire, England) is traced from the late 1st to the mid-3rd century AD. Three successive periods of building with their associated finds of artefacts and biological remains are described and interpreted with provisional reconstructions of the buildings. Links are provided to a copy of the Integrated Archaeological Database (IADB), archived by the Archaeology Data Service, which holds the primary excavation and finds records.

Heritage property, tourism and the UK Disability Discrimination Act

Heritage tourism depends on a physical resource based primarily on listed buildings and scheduled monuments. Visiting or staying in a historic building provides a rich tourism experience, but historic environments date from eras when access for disabled people was not a consideration. Current UK Government policy now promotes social inclusion via an array of equal opportunities, widening participation and anti-discrimination policies. Historic environments enjoy considerable legislative protection from adverse change, but now need to balance conservation with public access for all. This paper discusses the basis of research being undertaken by The College of Estate Management funded by the Mercers Company of London and the Harold Samuel Trust. It assesses how the 1995 Disability Discrimination Act has changed the legal obligations of owners/operators in managing access to listed buildings in tourism use. It also examines the key stakeholders and power structures in the management of historic buildings and distinguishes other important players in the management process.