Seminarvortrag Herr Christian Budde, Universität Nijmegen: "Operator Algebras and Unbounded Self-Adjoint Operators"
LMS 4 - Raum 312 - Diskussionsraum
The standard proof of the spectral theorem for unbounded self-adjoint operators on a Hilbert space (due to von Neumann) is to use projection-valued measures and the Cayley transform. Another approach (suggested by Woronowicz) is based on multiplier algebras and the "bounded transform", which yields a bijective correspondence between unbounded self-adjoint operators and self-adjoint pure contractions. Moreover, one obtains a relation between the spectrum of such an unbounded self-adjoint operator and the spectrum of its bounded transform. In addition, one can look at unbounded operators that are "close" to a set of bounded operators, i.e., the theory of affiliated operators, also originating with von Neumann. In particular, one can relate a given unbounded self-adjoint operator to a von Neumann algebra. This relation can neatly be expressed in terms of the bounded transform, too.
Einladender: Prof. Haase