Banach algebras generated by an invertible isometry of an LpL^p-space

We provide a complete description of those Banach algebras that are generated by an invertible isometry of an $L^p$-space together with its inverse. Examples include the algebra $PF_p(\mathbb{Z})$ of $p$-pseudofunctions on $\mathbb{Z}$, the commutative $C^*$-algebra $C(S^1)$ and all of its quotients, as well as uncountably many `exotic' Banach algebras. We associate to each isometry of an $L^p$-space, a spectral invariant called `spectral configuration', which contains considerably more information than its spectrum as an operator. It is shown that the spectral configuration describes the isometric isomorphism type of the Banach algebra that the isometry generates together with its inverse. It follows from our analysis that these algebras are semisimple. With the exception of $PF_p(\mathbb{Z})$, they are all closed under continuous functional calculus, and their Gelfand transform is an isomorphism. As an application of our results, we show that Banach algebras that act on $L^1$-spaces are not closed under quotients. This answers the case $p=1$ of a question asked by Le Merdy 20 years ago.Comment: 36 pages. Changes in v2: the results of Section 2 have been improved and extended, so they were removed to be included elsewhere. We showed that every H\"older exponent not equal to 2 is what we called 'regular', so this notion does not appear anymore. Fixed a number of typos, improved presentation, and added references. Changes in v3: added a new section with an application. Updated reference

Study of Extra Space Dimensions in Vector Boson Pair Production at LEP

Recent theoretical scenarios propose that quantum gravity effects may manifest at LEP energies by means of gravitons that couple to Standard Model particles and propagate into extra space dimensions. These predictions are checked against the most recent experimental results on photon, W and Z pair production. No deviations from the Standard Model expectations are found and limits of the order of 1 TeV on the scale of these models are set.Comment: 6 pages, 1 figur

James Stirling and the Tate Gallery Project in Albert Dock, Liverpool, 1982-88

El proyecto de James Stirling para adecuar el viejo almacén de Albert Dock para la Tate Gallery en Liverpool contenía dos niveles de intervención. El primero afectó a la intervención en su interior, que el arquitecto pudo desarrollar, coincidiendo en el tiempo con un momento de madurez personal y con el final de algunas obras claves de su trayectoria. Analizaremos las estrategias que Stirling utilizó para organizar el programa museístico, poner en valor la herencia estructural del proyecto de Jesse Hartley, sin renunciar a las mejores condiciones expositivas que la experiencia en el diseño de instalaciones similares le había permitido alcanzar. El segundo nivel de intervención, cuya propuesta fue rechazada y no pudo realizar, contemplaba el proyecto de nuevos accesos y conexiones con el viejo edificio. Fue una época en la que las autoridades estaban apostando por la readecuación y rehabilitación de toda la zona de los docks, de la que Albert Dock era y es la joya de la corona. Analizaremos los contenidos gráficos y escritos del irrealizado croquis de 1982 y veremos la aspiración de Stirling de vincular la visibilidad del museo con la propia historia de la ciudad y la arqueología vital de su propia memoria, planteando estrategias formales que, aun estando presentes en parte en otras obras, muestran una innovación que surge del diálogo con las arquitecturas y los paisajes preexistentes que sirven de soporte al proyecto.James Stirling’s project to adapt the abandoned Albert Dock warehouse for the Tate Gallery in Liverpool involved two levels of action. The first affected the inside of the building, a task that the architect was able to complete, coinciding in time with his personal maturity and with the completion of some key works in his career. We analyse the strategies Stirling used to organise the museum project, showcasing the structural legacy of Jesse Hartley’s project without renouncing the best exhibition conditions that his experience in designing similar premises had allowed him to reach. The second action level, one he could not bring to fruition because the proposal was rejected, contemplated new entrances to and connections with the old building. It was an era in which the authorities were focused on readapting and restoring the entire dock area, of which the Albert Dock was –and is– the crown jewel. We analyse the drawings and notes for the unachieved 1982 proposal, which reveal Stirling’s aspiration of linking the visibility of the museum with the city’s own history and the essential archaeology of his own memory. We can see how he formulated formal strategies that, although partially present in other works, show an innovation that arises from the dialogue with the pre–existing architectures and landscapes that anchor the project