Current research project (MTM2014-57838-C1 & C2)

Project title: Linear and non linear functional analysis in finite and infinite dimensions.

Joint Project Coordinator: Bernardo Cascales

Murcia Project Coordinator: Matías Raja

Valencia Project Coordinator 1: Manuel Maestre

Valencia Project Coordinator 2: Domingo García

Researchers:

Universidad de Murcia: Bernardo Cascales, José Orihuela, Matías Raja, Antonio José Pallarés Ruiz, Gustavo Garrigos .
Universidad de Valencia: Manuel Maestre, Domingo García, Jesús Ferrer, Pablo Sevilla, .
Universidad Politécnica de Cartagena: Carlos Angosto.
Universidad Politécnica de Valencia: Vicente Montesinos, Antonio José Guirao.
Czech Academy of Sciences: Marian Fabian.
Unviersität Oldenburg: Andreas Defant.
Universidad de Buenos Aires: W. Schachermayer.
Kent State University: Richard M. Aron.
Kharkiv V. N. Karazin National University: Volodymir Kadets.

Summary:

This coordinated Project is the culmination of a fruitful long-standing relationship between the Functional Analysis Groups from Murcia and Valencia. This coordinated project aims to give a suitable response to the call’s demand which claims that coordinated projects with powerful scientific coordinated plans will be promoted. Both groups have had long trajectories that have been scientifically and financially successful. They are both versatile groups: Murcia’s group stands out by a strong profile on topology, measure theory and geometry of Banach spaces; while Valencia’s one is noteworthy by his work on non-linear analysis and complex analysis on infinite dimensions. The relationship as well as the complementation between the research lines of both groups support their interaction, and opens the door to new challenges in this project. We beg for research, evidenced by high impact publications, the participation of assiduous researchers and the incorporation of new generations as Main Researchers, pluridisciplinarity and internationalization. In this this project with shall deal with the following topics of research:

• Dirichlet series.: We will study here Dirichlet series and its interaction with harmonic analysis and complex analysis in both finite and infinite dimensions, and also with analytic number theory..
• Infinite dimensional analysis and topology:We will study topological and geometrical tools in Banach spaces with applications to quantitative results, structure of convex sets, renorming in Banach spaces and strong generation of spaces by reflexive and superreflexive Banach spaces.
• Banach algebras and spaces of polynomials: We wil study the space of maximal ideals of Banach algebras of holomorphic functions and polynomials define on complex Banach spaces.
• Optimization We will study the Bishop-Phelps-Bollobás property and one-side James theorems that naturaly appears as tools for some questions in the context of finnancial mathematics..
• We will study here the approximation of elements of a Banach spaces by linear combination of N elements of a given basis, in particular, we will study greedy algoritms We will study the Bishop-Phelps-Bollobás property and one-side James theorems that naturaly appears as tools for some questions in the context of finnancial mathematics..
• Risk measures We will study how to apply our results regarding convex weak* closed cones in the proofs of the fundamental theorem of asset pricing.