Closable multipliers

Let $(X,\mu)$ and $(Y,\nu)$ be standard measure spaces. A function $\nph\in L^\infty(X\times Y,\mu\times\nu)$ is called a (measurable) Schur multiplier if the map $S_\nph$, defined on the space of Hilbert-Schmidt operators from $L_2(X,\mu)$ to $L_2(Y,\nu)$ by multiplying their integral kernels by $\nph$, is bound-ed in the operator norm. The paper studies measurable functions $\nph$ for which $S_\nph$ is closable in the norm topology or in the weak* topology. We obtain a characterisation of w*-closable multipliers and relate the question about norm closability to the theory of operator synthesis. We also study multipliers of two special types: if $\nph$ is of Toeplitz type, that is, if $\nph(x,y)=f(x-y)$, $x,y\in G$, where $G$ is a locally compact abelian group, then the closability of $\nph$ is related to the local inclusion of $f$ in the Fourier algebra $A(G)$ of $G$. If $\nph$ is a divided difference, that is, a function of the form $(f(x)-f(y))/(x-y)$, then its closability is related to the ``operator smoothness'' of the function $f$. A number of examples of non closable, norm closable and w*-closable multipliers are presented.

On the spectrum of frequently hypercyclic operators

A bounded linear operator $T$ on a Banach space $X$ is called frequently hypercyclic if there exists $x\in X$ such that the lower density of the set $\{n\in\N:T^nx\in U\}$ is positive for any non-empty open subset $U$ of $X$. Bayart and Grivaux have raised a question whether there is a frequently hypercyclic operator on any separable infinite dimensional Banach space. We prove that the spectrum of a frequently hypercyclic operator has no isolated points. It follows that there are no frequently hypercyclic operators on all complex and on some real hereditarily indecomposable Banach spaces, which provides a negative answer to the above question.

Norm attaining operators and pseudospectrum

It is shown that if $11$, the operator $I+T$ attains its norm. A reflexive Banach space $X$ and a bounded rank one operator $T$ on $X$ are constructed such that $\|I+T\|>1$ and $I+T$ does not attain its norm.

A short proof of existence of disjoint hypercyclic operators

We give a short proof of existence of disjoint hypercyclic tuples of operators of any given length on any separable infinite dimensional Fr\'echet space. Similar argument provides disjoint dual hypercyclic tuples of operators of any length on any infinite dimensional Banach space with separable dual.

Operators, commuting with the Volterra operator, are not weakly supercyclic

We prove that any bounded linear operator on $L_p[0,1]$ for $1\leq p

Observation of K-Shell Soft X Ray Emission of Nitrogen Irradiated by XUV-Free Electron Laser FLASH at Intensities Greater than 10(16) W/cm(2)

In the past few years, the development of light sources of the 4(th) generation, namely XUV/X-ray Free Electron Lasers provides to the scientific community outstanding tools to investigate matter under extreme conditions never obtained in laboratories so far. As theory is at its infancy, the analysis of matter via the self-emission of the target is of central importance. The characterization of such dense matter is possible if photons can escape the medium. As the absorption of K-shell X-ray transitions is minimal, it plays a key role in this study. We report here the first successful observation of K-shell emission of Nitrogen at 430 eV using an XUV-Free Electron Laser to irradiate solid Boron Nitride targets under exceptional conditions: photon energy of 92 eV, pulse duration of similar to 20 fs, micro focusing leading to intensities larger than 10(16) W/cm(2). Using a Bragg crystal of THM coupled to a CCD, we resolved K-shell line emission from different charge states. We demonstrate that the spectroscopic data allow characterization of electron heating processes when X-ray radiation is interacting with solid matter. As energy transport is non-trivial because the light source is monochromatic, these results have an important impact on the theory. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Conditions for efficient and stable ion acceleration by moderate circularly polarized laser pulses at intensities of 10(20) W/cm(2)

Conditions for efficient and stable ion radiation pressure acceleration (RPA) from thin foils by circularly polarized laser pulses at moderate intensities are theoretically and numerically investigated. It is found that the unavoidable decompression of the co-moving electron layer in Light-Sail RPA leads to a change of the local electrostatic field from a

'A new sword on an old anvil': W.B.Yeats, Robert Graves and the Anglo-Irish Tradition

Throughout his writing life, Robert Graves was consistently and often publicly hostile to the work of W.B. Yeats, whilst still also owing a considerable debt to the older poet (who he never met). This essay explores Graves' complex responses to Yeats, arguing that his antagonism may be understood in the light of his own Anglo-Irish background, and is implicated in his relations with his father, Alfred Perceval Graves, as well as his experience of the First World War. Probing the suggestiveness of Graves's claim in 1959 that his poems 'remain true to the Anglo-Irish poetic tradition into which I was born', it traces the relation between Yeats and Graves through correspondence, critical writings, and through a comparative reading of Yeats's A Vision and Graves's The White Goddess, and reveals underlying similarities in their critical and mythological thinking in spite of Graves's public disavowal of the Yeatsian aesthetic.

Review of The New Punitiveness: Trends, Theories, Perspectives , edited by J Pratt, D Brown, M Brown, S Hallsworth and W Morrison

Book Review

W(h)ither New Age studies? The uses of ethnography in a contested field of scholarship

Since the 1980s, there has existed a field of scholarly inquiry into a range of phenomena termed New Age. The relative lack of ethnographic studies in this field was identified several years ago, in response to research that focused merely on the discourses within alleged key writings. However, the employment of ethnographic methods does not by itself resolve the problems inherent in other modes of research; attention also has to be paid to how ethnography is used in practice. This article examines ethnographies of the New Age in terms of the extent to which they contextualize data within their immediate social frames, by paying attention to actors’ practices and interactions, and to the ways in which beliefs and discourses are constructed and contested. The article demonstrates the strong tendency among New Age ethnographic studies to veer from ‘the social’ and to rest instead on analytically problematic conceptualizations of agency. It argues that epistemological revision is required to form the basis of a more sociologically adequate understanding of the phenomena addressed.