Grant: Discovery Grants Program - Individual

This proposal is in Functional Analysis and is mainly devoted to the investigation of structural properties ofinfinite dimensional Banach spaces and of bounded operators acting on them.The first project continues a very successful investigation initiated in the previous grant proposal and deals with a new notion of invariance for bounded linear operators. We call this new notion ""almost invariance"" and examine under which condition bounded operators have non-trivial almost invariant subspaces.The second project deals with the construction of Banach spaces without approximation property. We areexamining conditions to obtain these constructions inside Banach spaces from certain large classes of spaces.The third project deals with the construction of a Banach space with very unexpected properties: it hasnon-trivial type, yet it contains no copy of well known classical spaces or of a reflexive space.