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.

Botanising women : transmission, translation and European exchange

This issue of the Journal of Literature and Science is a special issue entitled ‘Women and Botany’ edited by Sam George and Alison E. Martin.

‘These changes and accessions of knowledge’: translation, scientific travel writing and modernity - Alexander von Humboldt's Personal Narrative

A second English translation of Alexander von Humboldt's account of travel to South America, the Relation historique (1814–25), was published between 1852 and 1853. Appearing some 30 years after the first seven-volume translation (1814–29) by Helen Maria Williams, this second rendering of the Personal Narrative by Thomasina Ross was an abridged version that aimed to make Humboldt's travelogue more relevant to the mid-century reader. This translation has largely been overlooked by Humboldt scholars, despite it being a far more affordable, accessible and popular edition. I discuss here how Ross's revisions can be understood within a larger process of rereading and revision that responded to critics’ assessments of the first translation. Emphasising the status of the Personal Narrative as a text in flux, I assess how Ross modernised it to meet the demands of a new readership, recasting the image that Humboldt had constructed of himself as a travelling scientist, scientific writer and member of the international scientific community.

Natural effusions: Mrs J. Howorth’s English translation of Albrecht von Haller’s Die Alpen

Albrecht von Haller's Die Alpen [The Alps] was an immensely popular piece of early eighteenth-century poetry, yet it took more than half a century to be translated into English. In this article I examine Mrs J. Howorth's prose rendering of it in her translated collection The Poems of Baron Haller (1794) and analyse how the translation itself reflects late-eighteenth-century scientific, political and aesthetic concerns, notably through the influence of Linnaeus and Jean-Jacques Rousseau. Secondly, I explore how Howorth constructed a public image of herself as a female consumer and producer of botanical literature, and argue that her translation constitutes an early example of British women's increasing engagement in science through the activity of translation.

Authoriality in poetic translation. The case of Amelia Rosselli's practice

This article provides a historical and theoretical contextualization of Amelia Rosselli's practice of translation. Some hitherto neglected Rosselli translations from John Berryman will be examined to ascertain the role played by translation in her multilingual oeuvre. My analysis builds upon recent explorations of translingual authors' translating practice informed by Deleuze and Guattari's seminal Kafka: pour une littérature mineure. It aims to achieve an understanding of the aesthetic of Rosselli's trilingualism and the function of translation within the author's minorizing project.

'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function

In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = n¡® for its connection to the Riemann zeta function on the line 1, 'f is bounded with k'f k = ³(®). For the unbounded case, we show that 'f : M2 ! M2 where M2 is the subset of l2 of multiplicative sequences, for many f 2 M2. Consequently, we study the `quasi'-norm sup kak = T a 2M2 k'fak kak for large T, which measures the `size' of 'f on M2. For the f(n) = n¡® case, we show this quasi-norm has a striking resemblance to the conjectured maximal order of j³(® + iT )j for ® > 12 .

Symmetric stability of compressible zonal flows on a generalized equatorial β plane

Sufficient conditions are derived for the linear stability with respect to zonally symmetric perturbations of a steady zonal solution to the nonhydrostatic compressible Euler equations on an equatorial � plane, including a leading order representation of the Coriolis force terms due to the poleward component of the planetary rotation vector. A version of the energy–Casimir method of stability proof is applied: an invariant functional of the Euler equations linearized about the equilibrium zonal flow is found, and positive definiteness of the functional is shown to imply linear stability of the equilibrium. It is shown that an equilibrium is stable if the potential vorticity has the same sign as latitude and the Rayleigh centrifugal stability condition that absolute angular momentum increase toward the equator on surfaces of constant pressure is satisfied. The result generalizes earlier results for hydrostatic and incompressible systems and for systems that do not account for the nontraditional Coriolis force terms. The stability of particular equilibrium zonal velocity, entropy, and density fields is assessed. A notable case in which the effect of the nontraditional Coriolis force is decisive is the instability of an angular momentum profile that decreases away from the equator but is flatter than quadratic in latitude, despite its satisfying both the centrifugal and convective stability conditions.

Some uniform stability and convergence results for integral equations on the real line and projection methods for their solution

The paper considers second kind equations of the form (abbreviated x=y + K2x) in which and the factor z is bounded but otherwise arbitrary so that equations of Wiener-Hopf type are included as a special case. Conditions on a set are obtained such that a generalized Fredholm alternative is valid: if W satisfies these conditions and I − Kz, is injective for each z ε W then I − Kz is invertible for each z ε W and the operators (I − Kz)−1 are uniformly bounded. As a special case some classical results relating to Wiener-Hopf operators are reproduced. A finite section version of the above equation (with the range of integration reduced to [−a, a]) is considered, as are projection and iterated projection methods for its solution. The operators (where denotes the finite section version of Kz) are shown uniformly bounded (in z and a) for all a sufficiently large. Uniform stability and convergence results, for the projection and iterated projection methods, are obtained. The argument generalizes an idea in collectively compact operator theory. Some new results in this theory are obtained and applied to the analysis of projection methods for the above equation when z is compactly supported and k(s − t) replaced by the general kernel k(s,t). A boundary integral equation of the above type, which models outdoor sound propagation over inhomogeneous level terrain, illustrates the application of the theoretical results developed.