Research Team / Research Group Name (if any)
910346 Operadores , estructura y geometría de espacios de Banach
Brief description of the Research Team / Research Group / Department
Banach and Hilbert spaces, Operators, Banach lattices.
Research lines / projects proposed
This research project is included in the field of Mathematical Analysis, covering topics of Functional Analysis like Operator Theory and analytical techniques to study the geometry of Banach spaces. The main interests are focused around the lines:<br />1) Operator theory. In this framework, we focuses on the study of linear and bounded operators acting primarily in Hilbert spaces, the main issue to be addressed is to determine the structure of the given operator " for example, breaking it down in simpler operators, of simpler analysis, having as motivating goal the Invariant Subspace Problem. Operator Algebras are considered in this context, mainly in relation to understand structures of algebras generated by particular operators.<br />2) Geometry of Banach space and Banach lattices. While the study of geometry of Banach spaces is nowadays a classical subject, Banach lattices play an important role in order to determine the interplay about the properties of those operators acting on then and the underlined structure.<br /><br />The PI Eva A. Gallardo and some research members are faculty members of the research institute Instituto de Ciencias Matemáticas ICMAT, depending on the National Research Council CSIC and the universities Autónoma de Madrid, Carlos III and Complutense .ICMAT has been awarded with the distinction of Severo Ochoa Center in Research & Development (by the Government of Spain).