, Javier Parcet (dir. tes.) 
The goal of this thesis is to study an specific kind of algebras, known as von Neumann algebras, with methods coming from real analysis. These methods include the theory of Fourier multipliers, interpolation and maximal operators, among others. Each of these topics is well-stablished in mathematical analysis, not only for their intrinsic value but also for their wide-ranging applications across various fields in mathematics. Here, we aim to investigate how these techniques can be applied within the framework of von Neumann algebras
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