Pedro Tradacete: Free complex Banach lattices

Data: sexta-feira, 2 de dezembro de 2022, às 9h30.

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

Pedro Tradacete (Instituto de Ciencias Matemáticas - CSIC)

Título:  Free complex Banach lattices

Resumo:   We will show how the construction of the free Banach lattice generated  by a real Banach space can be extended to the complex setting. In other words, we will show that for every complex Banach space E there is a complex Banach lattice FBL_C[E] containing a linear isometric copy of E and satisfying the universal property that every operator from E to a complex Banach lattice admits a unique lattice homomorphism extension to an operator from FBL_C[E], without  increasing the norm. We will see that free complex Banach lattices have analogous properties to those of their real counterpart. However, examples of non-isomorphic complex Banach spaces E and F can be given so that the corresponding free complex Banach lattices are lattice isometric. This is based on joint work with David de Hevia.