Differential structure of the Thompson components of selfadjoint operators

Different equivalence relations are defined in the set L(H)s of self- adjoint operators of a Hilbert space H in order to extend a very well known relation in the cone of positive operators. As in the positive case, for a G L(H)s the equivalence class Ca admits a differential structure, which is compatible with a complete metric defined on Ca. This metric coincides with the Thompson metric when a is positive.Fil: Fongi, Guillermina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentin

Projections in operator ranges

If \H is a Hilbert space, $A$ is a positive bounded linear operator on \cH and \cS is a closed subspace of \cH, the relative position between \cS and A^{-1}(\cS \orto) establishes a notion of compatibility. We show that the compatibility of (A,\cS) is equivalent to the existence of a convenient orthogonal projection in the operator range $R(A^{1/2})$ with its canonical Hilbertian structure

Schur complements in Krein spaces

The aim of this work is to generalize the notions of Schur complements and shorted operators to Krein spaces. Given a (bounded) J-selfadjoint operator A (with the unique factorization property) acting on a Krein space H and a suitable closed subspace S of H, the Schur complement A/[s]of A to S is defined. The basic properties of A/ are developed and different characterizations are given, most of them resembling those of the shorted of (bounded) positive operators on a Hilbert space.Fil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Matemáticas; ArgentinaFil: Martinez Peria, Francisco Dardo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentin

On the geometry of normal projections in Krein spaces

Let $\mathcal{H}$ be a Krein space with fundamental symmetry $J$. Along this paper, the geometric structure of the set of $J$-normal projections $\mathcal{Q}$ is studied. The group of $J$-unitary operators $\mathcal{U}_J$ naturally acts on $\mathcal{Q}$. Each orbit of this action turns out to be an analytic homogeneous space of $\mathcal{U}_J$, and a connected component of $\mathcal{Q}$. The relationship between $\mathcal{Q}$ and the set $\mathcal{E}$ of $J$-selfadjoint projections is analized: both sets are analytic submanifolds of $L(\mathcal{H})$ and there is a natural real analytic submersion from $\mathcal{Q}$ onto $\mathcal{E}$, namely $Q\mapsto QQ^\#$. The range of a $J$-normal projection is always a pseudo-regular subspace. Then, for a fixed pseudo-regular subspace $\mathcal{S}$, it is proved that the set of $J$-normal projections onto $\mathcal{S}$ is a covering space of the subset of $J$-normal projections onto $\mathcal{S}$ with fixed regular part.Comment: 19 pages, accepted for publication in the Journal of Operator Theor

La professionalizzazione atipica della consulenza di management : il ruolo delle associazioni e delle organizzazioni

The study of professionalization's process is one of the most important themes of the sociology of work, which has given birth to the debate on professional groups since the contribution of Wilensky (1964). However, the growth of knowledge work which does not recognise themselves in the typical evolution of regulated professions has put in question the heuristic capacity of Wilensky's model, especially because the role of professional associations declines in favour of market and organisations. The article aims at discussing these issues, seeing them from the point of view of management consulting. At the light of recent changes in the public regulation of non-regulated professionals (L. 4/2013), it examines the role of professional associations in an atypical professionalization, which relies on market's success and branding more than collective participation in peer bodies.Lo studio del processo di professionalizzazione è uno dei temi portanti della sociologia del lavoro, che fin dal celebre contributo di Wilensky (1964) ha segnato lo sviluppo del dibattitto sull'evoluzione dei gruppi professionali. Tuttavia, la crescita dei cosiddetti knowledge worker che non si riconoscono nel percorso tipico delle professioni regolamentate, ha messo in crisi la capacità euristica del modello proposto da Wilensky, proprio perché il ruolo una volta svolto dalle associazioni professionali è sempre più giocato dal mercato e dalle organizzazioni. Il presente contributo vuole discutere queste problematiche, affrontandole dal punto di vista di una professione emergente come la consulenza di management. Alla luce dei recenti cambiamenti introdotti nella regolazione pubblica delle professioni non regolamentate (L. 4/2013), si discuterà il ruolo delle associazioni professionali in un processo di professionalizzazione atipico, che passa prevalentemente per il successo di mercato e la definizione di strategie di branding più che attraverso la partecipazione collettiva a organismi formati da pari

Solidarity Purchasing Groups

Solidarity Purchasing Groups (GAS) movement is a peculiar bottom up social innovation that has been spreading over the past 20 years in Italy. It is composed mostly of self-organised groups of citizens who collectively buy from small organic producers in Italy. They promote several practices that sustain the alternative food networks in the country, such as: solidarity and critical consumption, organic and km-0 productions as ways to promote environment protection, respect of labour regulation and fair economic relations. Several authors have recognised their role in reducing the marginalization of small and micro farms in the country (Forno and Graziano, 2014; Grasseni, 2014). The historical foundation of GAS can be traced back to the 19th century, when mutual purchasing groups had been promoted in the experience of consumers' cooperatives. More recently, the NoGlobal movement and the expansion of fair trade during the '90s have favoured the progressive increase of consumerism awareness among the middle classes (both in terms of purchasing power and in terms of cultural capital) that sustained the progressive growth of the GASs movement. GASs are now in a mature phase of the social innovation cycle and new more institutionalised forms (such as emporiums and formal associations) have now been established next to the original informal groups of consumers. The aim of this paper is to describe origins, features and transformations of the GASs movement in Italy. Our analysis is based on documents, materials and interviews out of WP7 qualitative phase in order to sketch a case study about Solidarity Purchasing Group. Between September 2015 and January 2016 35 interviews have been conducted with social innovators belonging to 35 GASs, distributed nation-wide. GASs have been selected randomly, stratifying the sample on the basis of a composite index aimed to capture the vulnerability of the contexts, being classified as low, medium and high vulnerable territories. The Italian team has interviewed at least ten social innovators for each type of context. In order to fully understand the life cycle of the social innovation and to trace the historical foundation of GASs movement, starting from the original experience of mutual consumer cooperatives, we have also added up 7 key-informant interviews with national and local representatives of GAS movement and with academic experts