Unitarily invariant norms and tensor products of maximal injective von Neumann subalgebras

This dissertation consists of four contributions to the study of von Neumann algebras. In the first part, we set up a representation theorem for unitarily invariant norms on finite factor von Neumann algebras. In the second part, we set up a representation theorem for unitarily invariant norms related to infinite factor von Neumann algebras. In the third part, we introduce a notion of completely singular von Neumann subalgebras and characterize the class of completely singular von Neumann subalgebras. In the fourth part, we study a longstanding open question on the tensor product of maximal injective von Neumann subalgebras. The first part of the dissertation is joint work with Don Hadwin, Eric Nordgren and Junhao Shen. The second part of the dissertation is joint work with Don Hadwin. This dissertation is partially supported by a University of New Hampshire dissertation fellowship