Multipliers and Transference on Noncommutative Lp-spaces: and the Relative Haagerup Property

This thesis deals with multipliers and transference on noncommutative Lp-spaces. It falls within the realm of noncommutative harmonic analysis, i.e. harmonic analysis on noncommutative spaces. Such spaces appear in several areas of mathematics, such as non-abelian groups, quantum groups, noncommutative geometry and the general theory of operator...

The CCAP for graph products of operator algebras

For a simple graph Γ and for unital C^*-algebras with GNS-faithful states (A_v,φ_v) for v∈VΓ, we consider the reduced graph product (A,φ)=⁎_v,Γ(A_v,φ_v), and show that if every C^*-algebra A_v has the completely contractive approximation property (CCAP) and...

The Structure of Hecke Operator Algebras

This dissertation is concerned with the study of the structure of certain deformations of operator algebras associated with Coxeter groups. These operator algebras, called Hecke C*-algebras and Hecke-von Neumann algebras, are operator algebraic completions of Iwahori-Hecke algebras. They occur as natural abstractions of certain endomorphism...

Non-commutative differentiation and estimates on operator integrals

In 2017 Martijn Caspers, Fedor Sukochev and Dmitriy Zanin published a paper which generalises the proof of Davies' 1988 paper, and thus resolves the Nazarov-Peller conjecture. The proofs of these papers have been presented in this thesis. They have been expanded with a proof that generalises the conjecture to arbitrary Schatten classes. The...

Quantum correlation matrices and Tsirelson’s problem: Previous work and three-player considerations

Tsirelson once claimed that the set of quantum correlations, defined by strategies of non-local two-player games, does not depend on which of two possible models is chosen: the tensor product model or the commuting operator model. He later came back from this claim, and the resulting conjecture is now known as Tsirelson’s problem. The problem...