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 .

Unraveling the electronic structures of low-valent naphthalene and anthracene iron complexes: x-ray, spectroscopic, and density functional theory studies

Naphthalene and anthracene transition metalates are potent reagents, but their electronic structures have remained poorly explored. A study of four Cp*-substituted iron complexes (Cp* = pentamethylcyclopentadienyl) now gives rare insight into the bonding features of such species. The highly oxygen- and water-sensitive compounds [K(18-crown- 6){Cp*Fe(η4-C10H8)}] (K1), [K(18-crown-6){Cp*Fe(η4-C14H10)}] (K2), [Cp*Fe(η4-C10H8)] (1), and [Cp*Fe(η4-C14H10)] (2) were synthesized and characterized by NMR, UV−vis, and 57Fe Mössbauer spectroscopy. The paramagnetic complexes 1 and 2 were additionally characterized by electron paramagnetic resonance (EPR) spectroscopy and magnetic susceptibility measurements. The molecular structures of complexes K1, K2, and 2 were determined by single-crystal X-ray crystallography. Cyclic voltammetry of 1 and 2 and spectroelectrochemical experiments revealed the redox properties of these complexes, which are reversibly reduced to the monoanions [Cp*Fe(η4-C10H8)]− (1−) and [Cp*Fe(η4-C14H10)]− (2−) and reversibly oxidized to the cations [Cp*Fe(η6-C10H8)]+ (1+) and [Cp*Fe(η6-C14H10)]+ (2+). Reduced orbital charges and spin densities of the naphthalene complexes 1−/0/+ and the anthracene derivatives 2−/0/+ were obtained by density functional theory (DFT) methods. Analysis of these data suggests that the electronic structures of the anions 1− and 2− are best represented by low-spin FeII ions coordinated by anionic Cp* and dianionic naphthalene and anthracene ligands. The electronic structures of the neutral complexes 1 and 2 may be described by a superposition of two resonance configurations which, on the one hand, involve a low-spin FeI ion coordinated by the neutral naphthalene or anthracene ligand L, and, on the other hand, a low-spin FeII ion coordinated to a ligand radical L•−. Our study thus reveals the redox noninnocent character of the naphthalene and anthracene ligands, which effectively stabilize the iron atoms in a low formal, but significantly higher spectroscopic oxidation state.

Legal outlier, again? U.S. felon suffrage: comparative and international human rights perspectives

The judiciousness of American felon suffrage policies has long been the subject of scholarly debate, not least due to the large number of affected Americans: an estimated 5.3 million citizens are ineligible to vote as a result of a criminal conviction. This article offers comparative law and international human rights perspectives and aims to make two main contributions to the American and global discourse. After an introduction in Part I, Part II offers comparative law perspectives on challenges to disenfranchisement legislation, juxtaposing U.S. case law against recent judgments rendered by courts in Canada, South Africa, Australia, and by the European Court of Human Rights. The article submits that owing to its unique constitutional stipulations, as well as to a general reluctance to engage foreign legal sources, U.S. jurisprudence lags behind an emerging global jurisprudential trend that increasingly views convicts’ disenfranchisement as a suspect practice and subjects it to judicial review. This transnational judicial discourse follows a democratic paradigm and adopts a “residual liberty” approach to criminal justice that considers convicts to be rights-holders. The discourse rejects regulatory justifications for convicts’ disenfranchisement, and instead sees disenfranchisement as a penal measure. In order to determine its suitability as a punishment, the adverse effects of disenfranchisement are weighed against its purported social benefits, using balancing or proportionality review. Part III analyzes the international human rights treaty regime. It assesses, in particular, Article 25 of the International Covenant on Civil and Political Rights (“ICCPR”), which proclaims that “every citizen” has a right to vote without “unreasonable restrictions.” The analysis concludes that the phrase “unreasonable restrictions” is generally interpreted in a manner which tolerates certain forms of disenfranchisement, whereas other forms (such as life disenfranchisement) may be incompatible with treaty obligations. This article submits that disenfranchisement is a normatively flawed punishment. It fails to treat convicts as politically-equal community members, degrades them, and causes them grave harms both as individuals and as members of social groups. These adverse effects outweigh the purported social benefits of disenfranchisement. Furthermore, as a core component of the right to vote, voter eligibility should cease to be subjected to balancing or proportionality review. The presumed facilitative nature of the right to vote makes suffrage less susceptible to deference-based objections regarding the judicial review of legislation, as well as to cultural relativity objections to further the international standardization of human rights obligations. In view of this, this article proposes the adoption of a new optional protocol to the ICCPR proscribing convicts’ disenfranchisement. The article draws analogies between the proposed protocol and the ICCPR’s “Optional Protocol Aiming at the Abolition of the Death Penalty.” If adopted, the proposed protocol would strengthen the current trajectory towards expanding convicts’ suffrage that emanates from the invigorated transnational judicial discourse.

Synthesis, chemical, electrochemical characterization of oxomolybdenum(V) complexes of 2-(3,5-dimethyl pyrazol-1-yl) benzothiazole ligand: crystal structure of ligand and oxomolybdenum(VI) complex and density functional theory (DFT) calculation

This work reports the ligational behavior of the neutral bidentate chelating molecule 2-(3,5-dimethyl pyrazol-1-yl) benzothiazole towards the oxomolybdenum(V) center. Both mononuclear complexes of the type (MoOX3L)-O-V and binuclear complexes of the formula (Mo2O4X2L2)-O-V (where X = Cl, Br) are isolated in the solid state. The complexes are characterized by elemental analyses, various spectroscopic techniques (UV-Vis IR), magnetic susceptibility measurement at room temperature, and cyclic voltammetry for their redox behavior at a platinum electrode in CH3CN. The mononuclear complexes (MoOX3L)-O-V are found to be paramagnetic while the binuclear complexes Mo2O4X2L2 are diamagnetic. Crystal and molecular structure of the ligand and the dioxomolybdenum complex (MoO2Br2L)-O-VI (obtained from the complex MoOBr3L during crystallization) have been solved by single crystal X-ray diffraction technique. Relevant DFT calculations of the ligand and the complex (MoO2Br2L)-O-VI are also carried out.