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Charakterizations of the Generators of Positive Semigroups on C*- and von Neumann Algebras

J. Rheinlaender

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Abstract

Generators of positive C_0-semigroups on C^*-algebras and C_0^*-semigroups on von Neumann algebras are examined. A characterization due to Bratteli and Robinson in the C_0-case is proven in the C_0^*-case. Under the additional assumptions of unitality and contractivity of the semigroup another characterization of the generator is given. This result is restated for the dual and predual semigroup.

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Generators of positive C_0-semigroups on C^*-algebras and C_0^*-semigroups on von Neumann algebras are examined. A characterization due to Bratteli and Robinson in the C_0-case is proven in the C_0^*-case. Under the additional assumptions of unitality and contractivity of the semigroup another characterization of the generator is given. This result is restated for the dual and predual semigroup.

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Available abstract

Generators of positive C_0-semigroups on C^*-algebras and C_0^*-semigroups on von Neumann algebras are examined. A characterization due to Bratteli and Robinson in the C_0-case is proven in the C_0^*-case. Under the additional assumptions of unitality and contractivity of the semigroup another characterization of the generator is given. This result is restated for the dual and predual semigroup.

Key concepts: Semigroup, Von Neumann architecture, Mathematics, Generator (circuit theory), Characterization (materials science), Dual (grammatical number), Pure mathematics, Von Neumann algebra

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