AM-algebras

David Muñoz-Lahoz (U Autonoma de Madrid)

Mar 21. 2025, 10:50 — 11:10

A Banach lattice $X$ is said to be an AM-space if $\|x \vee y\|=\max\{\|x\|, \|y\|\}$ for every $x,y \in X_+$. A classical theorem of Kakutani establishes that AM-spaces are precisely the closed sublattices of $C(K)$ spaces. This result provides an intrinsic characterization of the closed sublattices of $C(K)$. However, since $C(K)$ naturally carries a Banach algebra structure as well, a natural question arises: Can one characterize the closed subspaces of $C(K)$ that are simultaneously sublattices and subalgebras? In this talk, we demonstrate that such a characterization is indeed possible by adding a simple algebraic constraint to the AM-space condition. Introducing this interplay between the AM-space and algebraic structures will require a new characterization of the AM-space property.
(This is joint work with Pedro Tradacete.)
 

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Structures in Banach Spaces (Workshop)
Organizer(s):
Antonio Aviles (U Murcia)
Vera Fischer (U of Vienna)
Grzegorz Plebanek (U of Wroclaw)
Damian Sobota (U of Vienna)