arXiv subjects
Publications and source records attributed to Dan Virgil Voiculescu.
We prove a generalization for commuting $n$-tuples of unbounded self-adjoint operators and the Lorentz $(n,1)$ ideal,$n \ge 3$, of the Kato-Rosenblum theorem. The result is derived from earlier work for bounded operators [8]. Also, a very weak result for $n=2$ unbounded operators and other additional results are obtained.
Free probability analogs of the basics of extreme-value theory are obtained, based on Ando's spectral order. This includes classification of freely max-stable laws and their domains of attraction, using ``free extremal convolutions'' on the distributions. These laws coincide with the limit laws in the classical peaks-over-threshold approach. A free extremal projection-valued process over a measure-space is constructed, which is related to the free Poisson point process.