Jamison sequences in countably infinite discrete abelian groups

We extend the definition of Jamison sequences in the context of topological abelian groups. Then we study such sequences when the abelian group is discrete and countably infinite. An arithmetical characterization of such sequences is obtained, extending the result of Badea and Grivaux about Jamison sequences of integers. In particular, we prove that the sequence consisting of all elements of the group is a Jamison sequence. In the opposite, a sequence which generates a subgroup of infinite index in the group is never a Jamison sequence.Comment: 16 page

Statistique et mort industrielle : la fabrication du nombre de victimes de la silicose dans les houillères en France de 1946 à nos jours

La tardive reconnaissance de la silicose en 1945, en extension de la loi de 1919 sur les maladies professionnelles, a été conditionnelle au poste de travail, au secteur industriel, à la durée d’exposition. Les houillères nationalisées comme les autres entreprises ont ainsi pu relativiser les données issues de la radiologie et de l’épidémiologie, attribuer le mal à des maladies comme la tuberculose, imputer l’indemnisation à l’assurance-maladie ou aux autres assurances sociales. Le recours à l’immigration étrangère, aux emplois temporaires, aux rapatriements, a minimisé la morbidité et la mortalité observables. Le rôle de certains professeurs de médecine, la complicité du parti communiste à la Libération, la passivité des syndicats, l’impuissance de la sécurité sociale des mineurs, l’opacité statistique, l’obéissance à un système paternaliste, ont empêché la silicose de devenir une « cause ». Son histoire fournit une matrice de celle de l’amiante, des TMS ou des cancers professionnels aujourd’hui.The tardy recognition of silicosis in 1945, as a development of the 1919 law on occupational hazards, was related to the job, the industrial area, and the length of exposure. The nationalized coal basins like other companies were able to relativize radiology and epidemiology data, attribute the illness to tuberculosis, and impute indemnification to health or other social insurances. Recourse to foreign immigration, temporary jobs, and repatriation minimized the observable morbidity and mortality. The role of some professors of medicine, the complicity of the Communist Party at Liberation, the passivity of the trade unions, the weakness of miners’ social security, statistical opacity and being in thrall to the paternalist system prevented silicosis from becoming a “cause”. Its history provides a matrix for asbestos and professional RSI or cancers today

Escaping a neighborhood along a prescribed sequence in Lie groups and Banach algebras

It is shown that Jamison sequences, introduced in 2007 by Badea and Grivaux, arise naturally in the study of topological groups with no small subgroups, of Banach or normed algebra elements whose powers are close to identity along subsequences, and in characterizations of (self-adjoint) positive operators by the accretiveness of some of their powers. The common core of these results is a description of those sequences for which non-identity elements in Lie groups or normed algebras escape an arbitrary small neighborhood of the identity in a number of steps belonging to the given sequence. Several spectral characterizations of Jamison sequences are given, and other related results are proved