Operator algebras on Lp-spaces

Research Project, 2025 – 2028

This project sets out to explore the frontiers of operator algebras acting on Lp-spaces, an emergent area in functional analysis that extends the mathematical framework of quantum mechanics beyond the conventional case of Hilbert spaces.
This extension is motivated by the desire to understand the interplay between algebra, geometry and analysis for operators on Lp-spaces, as well as to capture phenomena that are not visible in the Hilbert space context. Over the past decade, the applicant has been a key contributor to advancing this field, with the primary aim now to further deepen our understanding of these operator algebras.For the next four years, the research will be led by the applicant and a PhD student, both embedded in the world-class operator algebras research group in Gothenburg.After an initial training phase, the PhD student will tackle the following projects in close collaboration with the applicant:(A) Establishing a Gelfand-Naimark type theorem that describes the structure of semisimple, commutative Lp-operator algebras through spectral invariants, expanding upon a special case previously resolved by the applicant.(B) Solving the famous pseudomeasure/convolver problem in abstract harmonic analysis by investigating general bicommutant theorems for Lp-operator algebras derived from group representations on Lp-spaces.(C) Demonstrating a deep connection between the algebraic and analytic nature of Lp-group algebras by proving uniqueness of their preduals.