Limit operators, collective compactness, and the spectral theory of infinite matrices

In the first half of this memoir we explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch and Silbermann (2004) and Lindner (2006)) and the concepts and results of the generalised collectively compact operator theory introduced by Chandler-Wilde and Zhang (2002). We build up to results obtained by applying this generalised collectively compact operator theory to the set of limit operators of an operator (its operator spectrum). In the second half of this memoir we study bounded linear operators on the generalised sequence space , where and is some complex Banach space. We make what seems to be a more complete study than hitherto of the connections between Fredholmness, invertibility, invertibility at infinity, and invertibility or injectivity of the set of limit operators, with some emphasis on the case when the operator is a locally compact perturbation of the identity. Especially, we obtain stronger results than previously known for the subtle limiting cases of and . Our tools in this study are the results from the first half of the memoir and an exploitation of the partial duality between and and its implications for bounded linear operators which are also continuous with respect to the weaker topology (the strict topology) introduced in the first half of the memoir. Results in this second half of the memoir include a new proof that injectivity of all limit operators (the classic Favard condition) implies invertibility for a general class of almost periodic operators, and characterisations of invertibility at infinity and Fredholmness for operators in the so-called Wiener algebra. In two final chapters our results are illustrated by and applied to concrete examples. Firstly, we study the spectra and essential spectra of discrete Schrödinger operators (both self-adjoint and non-self-adjoint), including operators with almost periodic and random potentials. In the final chapter we apply our results to integral operators on .

Spectral theory of Toeplitz and Hankel operators on the Bergman space A1

The Fredholm properties of Toeplitz operators on the Bergman space A2 have been well-known for continuous symbols since the 1970s. We investigate the case p=1 with continuous symbols under a mild additional condition, namely that of the logarithmic vanishing mean oscillation in the Bergman metric. Most differences are related to boundedness properties of Toeplitz operators acting on Ap that arise when we no longer have 1of Hankel operators on A1.

Commodity futures prices: more evidence on forecast power, risk premia and the theory of storage

In this paper, we examine the temporal stability of the evidence for two commodity futures pricing theories. We investigate whether the forecast power of commodity futures can be attributed to the extent to which they exhibit seasonality and we also consider whether there are time varying parameters or structural breaks in these pricing relationships. Compared to previous studies, we find stronger evidence of seasonality in the basis, which supports the theory of storage. The power of the basis to forecast subsequent price changes is also strengthened, while results on the presence of a risk premium are inconclusive. In addition, we show that the forecasting power of commodity futures cannot be attributed to the extent to which they exhibit seasonality. We find that in most cases where structural breaks occur, only changes in the intercepts and not the slopes are detected, illustrating that the forecast power of the basis is stable over different economic environments.

Interpersonal interaction and economic theory: the case of public goods

Interpersonal interaction in public goods contexts is very different in character to its depiction in economic theory, despite the fact that the standard model is based on a small number of apparently plausible assumptions. Approaches to the problem are reviewed both from within and outside economics. It is argued that quick fixes such as a taste for giving do not provide a way forward. An improved understanding of why people contribute to such goods seems to require a different picture of the relationships between individuals than obtains in standard microeconomic theory, where they are usually depicted as asocial. No single economic model at present is consistent with all the relevant field and laboratory data. It is argued that there are defensible ideas from outside the discipline which ought to be explored, relying on different conceptions of rationality and/or more radically social agents. Three such suggestions are considered, one concerning the expressive/communicative aspect of behaviour, a second the possibility of a part-whole relationship between interacting agents and the third a version of conformism.

Reaching the underbanked and unbanked in subsistence markets at the nexus of the formal and informal economy

It is estimated that globally over 2 billion people do not have a bank account, with many more in the developed and developing worlds ‘under-banked’, meaning they have limited access to financial services. Reaching the unbanked and underbanked with appropriate financial services is widely recognised as critical for future global economic growth and prosperity. Drawing upon multidimensional understandings of poverty, and framed by literature on poverty pools, traps and cycles, this paper explores the use of financial products and services in the developing world and critically reflects on their potential role in poverty alleviation and wider sustainable development. Discussions are illustrated with reference to qualitative empirical research undertaken in East and Southern Africa, and a sense-making of the lived financial experiences of low income individuals, households and communities.

Landscape change in central Latvia since the Iron Age: multi-proxy analysis of the vegetation impact of conflict, colonization and economic expansion during the last 2000 years

This study represents the first detailed multi-proxy palaeoenvironmental investigation associated with a Late Iron Age lake-dwelling site in the eastern Baltic. The main objective was to reconstruct the environmental and vegetation dynamics associated with the establishment of the lake-dwelling and land-use during the last 2,000 years. A lacustrine sediment core located adjacent to a Late Iron Age lake-dwelling, medieval castle and Post-medieval manor was sampled in Lake Āraiši. The core was dated using spheroidal fly-ash particles and radiocarbon dating, and analysed in terms of pollen, non-pollen palynomorphs, diatoms, loss-on-ignition, magnetic susceptibility and element geochemistry. Associations between pollen and other proxies were statistically tested. During ad 1–700, the vicinity of Lake Āraiši was covered by forests and human activities were only small-scale with the first appearance of cereal pollen (Triticum and Secale cereale) after ad 400. The most significant changes in vegetation and environment occurred with the establishment of the lake-dwelling around ad 780 when the immediate surroundings of the lake were cleared for agriculture, and within the lake there were increased nutrient levels. The highest accumulation rates of coprophilous fungi coincide with the occupation of the lake-dwelling from ad 780–1050, indicating that parts of the dwelling functioned as byres for livestock. The conquest of tribal lands during the crusades resulted in changes to the ownership, administration and organisation of the land, but our results indicate that the form and type of agriculture and land-use continued much as it had during the preceding Late Iron Age.

GM food purchase intentions: linking the theory of planned behaviour with consumer trust and stated choice

After the “European” experience of BSE and further food safety crises consumer trust is playing an increasingly important role in political and marketing decision making. This also relates to the area of consumer acceptance of GM food. This paper integrates consumer trust with the theory of planned behavior and a stated choice model to gain a more complete picture of consumer decision making. Preliminary results indicate that when GM products offer practical benefits to consumers acceptance may increase considerably. Furthermore, both trust and perceived benefits contribute significantly to explaining the level of acceptance.

The transaction cost economics theory of the family firm: family-based human asset specificity and the bifurcation bias

We develop a transaction cost economics theory of the family firm, building upon the concepts of family-based asset specificity, bounded rationality, and bounded reliability. We argue that the prosperity and survival of family firms depend on the absence of a dysfunctional bifurcation bias. The bifurcation bias is an expression of bounded reliability, reflected in the de facto asymmetric treatment of family vs. nonfamily assets (especially human assets). We propose that absence of bifurcation bias is critical to fostering reliability in family business functioning. Our study ends the unproductive divide between the agency and stewardship perspectives of the family firm, which offer conflicting accounts of this firm type's functioning. We show that the predictions of the agency and stewardship perspectives can be usefully reconciled when focusing on how family firms address the bifurcation bias or fail to do so.