Книга: Spectrum of a C*-algebra: C*-Algebra, Unitary Equivalence, Hilbert Space, Topological Space, Simple Module, Spectrum of a Ring, Locally Compact Group, Plancherel Theorem

High Quality Content by WIKIPEDIA articles! The spectrum of a C*-algebra or dual of a C*-algebra A, denoted A, is the set of unitary equivalence classes of irreducible *-representations of A. A *-representation ? of A on a Hilbert space H is irreducible if, and only if, there is no closed subspace K different from H and {0} which is invariant under all operators ?(x) with x ? A. We implicitly assume that irreducible representation means non-null irreducible representation, thus excluding trivial (i.e. identically 0) representations on one-dimensional spaces. As explained below, the spectrum A is also naturally a topological space this generalizes the notion of the spectrum of a ring.