Toeplitz operators with distributional symbols on Bergman spaces

We study the boundedness and compactness of Toeplitz operators Ta on Bergman spaces , 1 < p < ∞. The novelty is that we allow distributional symbols. It turns out that the belonging of the symbol to a weighted Sobolev space of negative order is sufficient for the boundedness of Ta. We show the natural relation of the hyperbolic geometry of the disc and the order of the distribution. A corresponding sufficient condition for the compactness is also derived.

A note on the Fredholm properties of Toeplitz operators on weighted Bergman spaces with matrix-valued symbols

We characterize the essential spectra of Toeplitz operators Ta on weighted Bergman spaces with matrix-valued symbols; in particular we deal with two classes of symbols, the Douglas algebra C+H∞ and the Zhu class Q := L∞ ∩VMO∂ . In addition, for symbols in C+H∞ , we derive a formula for the index of Ta in terms of its symbol a in the scalar-valued case, while in the matrix-valued case we indicate that the standard reduction to the scalar-valued case fails to work analogously to the Hardy space case. Mathematics subject classification (2010): 47B35,

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.

Toeplitz operators on Bergman spaces with locally integrable symbols

We study the boundedness of Toeplitz operators $T_a$ with locally integrable symbols on Bergman spaces $A^p(\mathbb{D})$, $1 < p < \infty$. Our main result gives a sufficient condition for the boundedness of $T_a$ in terms of some ``averages'' (related to hyperbolic rectangles) of its symbol. If the averages satisfy an ${o}$-type condition on the boundary of $\mathbb{D}$, we show that the corresponding Toeplitz operator is compact on $A^p$. Both conditions coincide with the known necessary conditions in the case of nonnegative symbols and $p=2$. We also show that Toeplitz operators with symbols of vanishing mean oscillation are Fredholm on $A^p$ provided that the averages are bounded away from zero, and derive an index formula for these operators.

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.

Behaviour change in the UK climate debate : an assessment of responsibility, agency and political dimensions

This paper explores the politics around the role of agency in the UK climate change debate. Government interventions on the demand side of consumption have increasingly involved attempts to obtain greater traction with the values, attitudes and beliefs of citizens in relation to climate change and also in terms of influencing consumer behaviour at an individual level. With figures showing that approximately 40% of the UK’s carbon emissions are attributable to household and transport behaviour, policy initiatives have progressively focused on the facilitation of “sustainable behaviours”. Evidence suggests however, that mobilisation of pro-environmental attitudes in addressing the perceived “value-action gap” has so far had limited success. Research in this field suggests that there is a more significant and nuanced “gap” between context and behaviour; a relationship that perhaps provides a more adroit reflection of reasons why people do not necessarily react in the way that policy-makers anticipate. Tracing the development of the UK Government’s behaviour change agenda over the last decade, we posit that a core reason for the limitations of this programme relates to an excessively narrow focus on the individual. This has served to obscure some of the wider political and economic aspects of the debate in favour of a more simplified discussion. The second part of the paper reports findings from a series of focus groups exploring some of the wider political views that people hold around household energy habits, purchase and use of domestic appliances, and transport behaviour-and discusses these insights in relation to the literature on the agenda’s apparent limitations. The paper concludes by considering whether the aims of the Big Society approach (recently established by the UK’s Coalition Government) hold the potential to engage more directly with some of these issues or whether they merely constitute a “repackaging” of the individualism agenda.

Why UK public lawyers need to be legal and political theorists

My aim in this article is to encourage UK public lawyers to engage with contemporary debates in legal, political and constitutional theory. My argument is motivated by three related concerns. First, there is an extricable link between these disciplines: behind every proposition of public law can be found a theory of law, govenment, the state and so on; secondly, public lawyers have historically neglected or fudged theory in their work; finally, a growing number of public lawyers are now using cutting-edge legal and political theories to fashion radical new understandings of the British constitution: other (more conservative-minded) public lawyers have no option, I argue, but to answer these new challenges. I illustrate my argument with reference to debates about Parliamentary sovereignty, the constitutional foundations of judicial review, political constitutionalism, and judicial deference.

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.

Addressee orientation in political speeches: tracing the dialogical 'other' in argumentative monologue

This article suggests that the addressees as the dialogical ‘other’ loom large in monological political speeches. However, political speeches are produced under conditions of addressee heterogeneity, i.e. the speakers do not actually know who they will be talking to. It will be argued that the addressees are nevertheless a crucial element in speakers’ context models, that speakers orientate towards imagined addressees and that certain aspects – what possible addressees may do, think or believe and that they are a part of an imagined community – are particularly relevant from the speakers’ point of view. An analysis of addressee orientation in political speeches aims at reconstructing speakers’ conceptualisations of possible addressees. The analysis reveals patterns of addressee orientation which suggest that the addressees are framed in terms of presumed nearness (i.e. agreement) or distance (i.e. disagreement) to the speakers. Both presumed agreement and disagreement will be discussed in terms of how the speakers aim to impose their default perspectives on the addressees. The analysis is based on examples from a substantial corpus of German chancellors’ political speeches from 1951-2001.

Human capital and growth under political uncertainty

In this paper we show how political uncertainty may impede economic growth by reducing public investment in the formation of human capital, and how this negative effect of political uncertainty can be offset by a government contract. We present a model of growth with accumulation of human capital and government investment in education. We show that in a country with an unstable political system the government is reluctant to invest in human capital. Low government spending on education negatively affects productivity and slows growth. Furthermore, a politically unstable economy may be trapped in a stagnant equilibrium. We also demonstrate the role of a government retirement contract. Public investment in education and economic growth are higher when the future retirement compensation of the government depends on the future national income, in comparison with investment under zero or fixed retirement compensation.