Analysis & Applications Seminar
Interactions between order and algebra in Functional Analysis
Speaker: David Muñoz Lahoz (UAM-ICMAT)Date: Friday, 26 June 2026 - 9:30Place: Aula 520, Módulo 17, Departamento de Matemáticas, UAM
Abstract:
In this talk, we will explore the interaction between order structures and products in functional analysis. More specifically, we will focus on Banach lattice algebras: Banach lattices that are also Banach algebras, and in which the product of positive elements is positive.
Following the roadmap proposed by A. W. Wickstead more than a decade ago, we will present several recent advances in the understanding of these objects. In particular, we will briefly discuss the new results obtained in this thesis on free Banach f-algebras, on Banach lattice algebras that admit a representation as subalgebras of spaces of continuous functions on compact spaces, and on the characterization of f-algebra products on AM- and AL-spaces.
After this, we will focus on a key question in the theory of Banach lattice algebras, which has been the central motivation for this thesis project: is every Banach lattice algebra representable inside a space of regular operators on an order-complete Banach lattice? If this were the case, we would have a result analogous to the classical Gelfand-Naimark-Segal theorem. Wickstead showed that, even in dimension 2, this question reduces to a nontrivial problem in operator theory. In this talk, we will explain some details of the solution to Wickstead’s problem obtained in this thesis, and how it yields a negative answer to the representation problem for Banach lattice algebras
