Noé de Rancourt: On subspaces of certain Orlicz sequence spaces

Data: sexta-feira, 16 de dezembro de 2022, às 11h00.

Formato híbrido: Sala A249 IME (Presencial). Google meet:

Noé de Rancourt (U. Lille)

Título:  On subspaces of certain Orlicz sequence spaces

Resumo:   Ferenczi and Rosendal conjectured two decades ago that every separable Banach space that is not isomorphic to a Hilbert space should have continuum-many pairwise non-isomorphic subspaces. After progress made by Cuellar Carrera, it only remains to prove it for near Hilbert spaces, that are, spaces whose geometric properties are very close to Hilbertspaces. In a common work with Ondřej Kurka, we proved that some Orlicz sequence spaces that are near Hilbert satisfy Ferenczi and Rosendal's conjecture. More precisely, we proved that Orlicz spaces associated with a regular enough Orlicz function which is "close" to t² should have asymptotically Hilbertian subspaces; such spaces have been proved by Anisca to have many subspaces. I will present the proof of our result, which involves a study of Banach-Mazur distances of finite-dimensional subspaces of Orlicz spaces to Hilbert spaces.