Automorphisms in spaces of continuous functions on Valdivia compacta

We show that there are no automorphic Banach spaces of the form C(K) with K continuous image of Valdivia compact except the spaces c0(I). Nevertheless, when K is an Eberlein compact of finite height such that C(K) is not isomorphic to c0(I), all isomorphism between subspaces of C(K) of size less than aleph_omega extend to automorphisms of C(K)

On Uniformly finitely extensible Banach spaces

We continue the study of Uniformly Finitely Extensible Banach spaces (in short, UFO) initiated in Moreno-Plichko, \emph{On automorphic Banach spaces}, Israel J. Math. 169 (2009) 29--45 and Castillo-Plichko, \emph{Banach spaces in various positions.} J. Funct. Anal. 259 (2010) 2098-2138. We show that they have the Uniform Approximation Property of Pe\l czy\'nski and Rosenthal and are compactly extensible. We will also consider their connection with the automorphic space problem of Lindenstrauss and Rosenthal --do there exist automorphic spaces other than $c_0(I)$ and $\ell_2(I)$?-- showing that a space all whose subspaces are UFO must be automorphic when it is Hereditarily Indecomposable (HI), and a Hilbert space when it is either locally minimal or isomorphic to its square. We will finally show that most HI --among them, the super-reflexive HI space constructed by Ferenczi-- and asymptotically $\ell_2$ spaces in the literature cannot be automorphic.Comment: This paper is to appear in the Journal of Mathematical Analysis and Application

Theory of "z"-linear maps

La teoría que se desarrolla en esta tesis contempla las aplicaciones lineales Z a través de tres diferentes puntos de vista: como objetos de una categoría, como herramientas homológicas y funciones. En este trabajo se introduce por primera vez una categoría de aplicaciones lineales Z (o de las secuencias exactas de los espacios de Banach), que designaremos Z. Identificamos tres tipos de objetos en Z: el objeto cero, los objetos singulares y cosingular, y algunos objetos universales. También abordamos el límite inductivo de aplicaciones lineales Z. Descubrimos dos hechos: es posible completar algunos diagramas de secuencias exactas y todos los objetos de Z definidos en un espacio separable, que puede ser visto como un límite inductivo. El cambio de un momento para considerar las aplicaciones lineales Z como funciones, lo que significa que este tipo de aplicaciones admiten representaciones de dimensión finita inductivas. Una herramienta fundamental en el problema de la extensión para los operadores de C ( K) por valor es el lema de Zippin, que caracteriza a los subespacios Y, ! X tal que cada operador de Y! C ( K ) se extiende a X (se dice que Y es casi complementado en X, o bien, en nuestros términos, que la extensión inducida por Y, ! X es casi trivial o C ( K ) trivial). La existencia de versiones convexas es precisamente lo que nos permite representar aplicaciones lineales Z como límites inductivos de mapas con rango de dimensión finita (esto es lo que llamamos a la representación de dimensión finita inductiva de F).The theory we develop in this memoir contemplates z-linear maps through three different points of view: as objects in a category, as homological tools, and functions. In this work we introduce for the first time a category of z-linear maps, which we shall denote Z. We identify three type of objects in Z: the object zero, the singular and cosingular objects, and some universal objects. We also tackle the inductive limit of z-linear maps. We uncover two facts: it is possible complete certain diagrams of exact sequences; and every object of Z defined on a separable space can be seen as an inductive limit. Shifting for a moment to consider z-linear maps as functions, that means that such maps admit inductive finite dimensional representations. A fundamental tool in the extension problem for C(K)-valued operators is Zippin’s lemma, that characterizes the subspaces Y ,! X such that every operator Y ! C(K) extends to X (it is said that Y is almost complemented in X; or, in our terms, that the induced extension by Y ,! X is almost-trivial or C(K)-trivial). The existence of convex versions is precisely what allows us to represent z-linear maps as inductive limits of maps with finite dimensional range (this is what we called inductive finite dimensional representation of F)

A case study from the un Peacekeeping mission in Lebanon

UIDB/04097/2020 UIDP/04097/2020This article presents a socio-linguistic analysis of interpreting in conflict zones and paints a picture of the limits on the interpreter s agency when working in the field. It focuses on the interpreter s behaviour towards cultural and linguistic barriers in communication between foreign military personnel and the civilian population in Lebanon. The aim is to analyse the level of agency that the interpreter has when working in a military deployment, taking into account the context and the narrative features that require mediation. Data were gathered through interviews with interpreters in Lebanon and analysed by applying narrative theory. Knowing and appreciating both the theoretical context and the linguistic and cultural barriers identified through the analysis are fundamental to understanding the difficult role that the interpreter-mediator plays in conflict settings and to reflecting on interpreter training that is appropriate to this context.publishersversionpublishe

Theory of "z"-linear maps

La teoría que se desarrolla en esta tesis contempla las aplicaciones lineales Z a través de tres diferentes puntos de vista: como objetos de una categoría, como herramientas homológicas y funciones. En este trabajo se introduce por primera vez una categoría de aplicaciones lineales Z (o de las secuencias exactas de los espacios de Banach), que designaremos Z. Identificamos tres tipos de objetos en Z: el objeto cero, los objetos singulares y cosingular, y algunos objetos universales. También abordamos el límite inductivo de aplicaciones lineales Z. Descubrimos dos hechos: es posible completar algunos diagramas de secuencias exactas y todos los objetos de Z definidos en un espacio separable, que puede ser visto como un límite inductivo. El cambio de un momento para considerar las aplicaciones lineales Z como funciones, lo que significa que este tipo de aplicaciones admiten representaciones de dimensión finita inductivas. Una herramienta fundamental en el problema de la extensión para los operadores de C ( K) por valor es el lema de Zippin, que caracteriza a los subespacios Y, ! X tal que cada operador de Y! C ( K ) se extiende a X (se dice que Y es casi complementado en X, o bien, en nuestros términos, que la extensión inducida por Y, ! X es casi trivial o C ( K ) trivial). La existencia de versiones convexas es precisamente lo que nos permite representar aplicaciones lineales Z como límites inductivos de mapas con rango de dimensión finita (esto es lo que llamamos a la representación de dimensión finita inductiva de F).The theory we develop in this memoir contemplates z-linear maps through three different points of view: as objects in a category, as homological tools, and functions. In this work we introduce for the first time a category of z-linear maps, which we shall denote Z. We identify three type of objects in Z: the object zero, the singular and cosingular objects, and some universal objects. We also tackle the inductive limit of z-linear maps. We uncover two facts: it is possible complete certain diagrams of exact sequences; and every object of Z defined on a separable space can be seen as an inductive limit. Shifting for a moment to consider z-linear maps as functions, that means that such maps admit inductive finite dimensional representations. A fundamental tool in the extension problem for C(K)-valued operators is Zippin’s lemma, that characterizes the subspaces Y ,! X such that every operator Y ! C(K) extends to X (it is said that Y is almost complemented in X; or, in our terms, that the induced extension by Y ,! X is almost-trivial or C(K)-trivial). The existence of convex versions is precisely what allows us to represent z-linear maps as inductive limits of maps with finite dimensional range (this is what we called inductive finite dimensional representation of F)