Endomorphism Semigroups and Lightlike Translations

Details Endomorphism Semigroups and Lightlike Translations Endomorphism Semigroups and Lightlike Translations

1995-05-30

arxiv.org/abs/funct-an/9505002v2

Mathematics

Operator Algebras

16 pages, Latex; minor corrections

Scientific paper

10.1007/BF00398300

Borchers and Wiesbrock have demonstrated certain results concerning the one-parameter semigroups of endomorphisms of von Neumann algebras that appear as lightlike translations in the theory of algebras of local observables. These results are abstracted and analyzed as essentially operator-theoretic. Criteria are then demonstrated for a spatial derivation of a von Neumann algebra to generate a one-parameter semigroup of endomorphisms. All this is combined to establish a von Neumann-algebraic converse to the Borchers-Wiesbrock results. This analysis is then applied to questions of isotony and covariance for local algebras.

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