On nearly isometric l1 -preduals

Organizer
María de los Ángeles Japón Pineda
Lugar
Seminario I (IMUS), Edificio Celestino Mutis
Autor
Lukasz Piasecki
Tipo de evento
Descripción


ABSTRACT
The notion of nearly isometric Banach spaces appeared for the first time in the celebrated book by Stefan Banach Th´eorie des op´erations lin´eaires, Warsaw, 1932. Recall that two isomorphic Banach spaces X and Y are said to be nearly isometric (or almost isometric) if d(X, Y ) := inf { || Ø || || Ø-1 ||: Ø   is an isomorphism from X onto Yo = 1.
For every predual X of `1 such that the standard basis in `1 is weak convergent, we give explicit models of all Banach spaces that are nearly isometric to X. We also present some illustrations and applications of our considerations.