2026-T3 Operator Algebras: Approximation, Rigidity and Dynamics

Organized by C. Houdayer, L. Ndekere & M. de la Salle

Operator algebras are self-adjoint subalgebras of the bounded operators on a Hilbert space and divide into two main classes: C∗-algebras and von Neumann algebras, according to whether one demands that they are closed in the norm topology or the weak operator topology.

When one first meets these algebras, they might look quite similar, but they have different natures as exemplified by the commutative case: via the Gelfand transform, abelian C∗-algebras are algebras of continuous functions vanishing at infinity on a locally compact Hausdorff space, while abelian von Neumann algebras are essentially bounded measurable functions on a measure space. These flavours persist in general. Topological concepts such as dimension and invariants such as K-theory pervade the study of C∗-algebras, while measure- theoretic style methods are often used to study von Neumann algebras.

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