von Neumann Factor

A von Neumann factor is a von Neumann algebra whose center consists only of scalar multiples of its identity. A finite-dimensional example is . A type factor is an infinite-dimensional factor with a faithful normal tracial state and no nonzero minimal projection. Its trace is normalized to take value 1 on the identity. A type factor has no nonzero finite projection, where a projection is finite when it is not equivalent to a proper subprojection through a partial isometry. The subtypes are distinguished by modular spectral invariants. For type , the intersection of the spectra of the modular operators associated with faithful normal weights is . Finite module dimensions over type factors define bifinite correspondences, while bicentralizers concern type factors.