Pervasive Algebras and Maximal Subalgebras.

A uniform algebra A on its Shilov boundary X is maximal if A is not C(X) and no uniform algebra is strictly contained between A and C(X) . It is essentially pervasive if A is dense in C(F) whenever F is a proper closed subset of the essential set of A. If A is maximal, then it is essentially pervasive and proper. We explore the gap between these two concepts. We show: (1) If A is pervasive and proper, and has a nonconstant unimodular element, then A contains an infinite descending chain of pervasive subalgebras on X . (2) It is possible to find a compact Hausdorff space X such that there is an isomorphic copy of the lattice of all subsets of N in the family of pervasive subalgebras of C(X). (3) In the other direction, if A is strongly logmodular, proper and pervasive, then it is maximal. (4) This fails if the word “strongly” is removed. We discuss examples involving Dirichlet algebras, A(U) algebras, Douglas algebras, and subalgebras of H∞(D), and develop new results that relate pervasiveness, maximality, and relative maximality to support sets of representing measures.

Organizational Frames for Professional Claims: Private Military Corporations and the Rise of the Military Paraprofessional

Corporations, nongovernmental organizations, and other organizational forms are major players in the sodal world. Recently, sociological scholarship on organizations has converged with research on the professions to discuss the ways in which professions are shaped or influenced by different organizational forms. In this article, I borrows from the notion of framing within social movement research to argue that organizational forms frame the bids of aspiring professionals. More specifically, I argue that certain organizational forms-such as that of the modern corporation-can aid would-be professionals in making their claims for professional recognition. Organizations do this, I argue, by providing aspiring professionals with a ready-made setting, rationale, and guarantees that make the newcomers more easily recognizable as professionals to outside audiences. I explore this argument by examining how the corporate form has facilitated private military contractors in their attempts to legitimate and develop this highly controversial new industry. The data are drawn from my interviews with private military contractors, state officials, and other interested parties surrounding private military corporations, as well as from archival data that detail the rise of the private military industry.