Compressions of free products of von Neumann algebras
Abstract
A reduction formula for compressions of von Neumann algebras arising as free products is proved. This shows that the fundamental group is all of the positive reals for some such algebras. Additionally, by taking a sort of free product with an unbounded semicircular element, continuous one parameter groups of trace scaling automorphisms on IIinfinity factors are constructed; this produces type III1 factors with core M tensor B(H), where M can be a full II1-factor without the Haagerup approximation property.
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