Operator Rings and Spectral Multiplicity
Operator algebra in Hilbert space has developed extensively from a variety of motivations and in several directions, beginning with the double-commutor theorem of von Neumann (1930). Von Neumann himself, in part in collaboration with F. J. Murray, founded during the ensuing two decades the theory of what he called simply “rings”, but which are known more specifically as “ W*-algebras” or “von Neumann algebras”. Here we shall follow von Neumann’s usage of the term “ring” when there appears to be no likelihood of confusion, and otherwise employ the term “ W*-algebra”, the “ W” referring to the weak topology, in which the algebra is closed, and the “*” to its self-adjointness.
KeywordsHilbert Space Cyclic Vector Boolean Ring Weak Operator Topology Spectral Multiplicity
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