Annihilators and Type Decomposition in C*-Algebras

Tristan Bice

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arXiv · 1310.4639

Annihilators and Type Decomposition in C*-Algebras

Tristan Bice

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Abstract

We initiate the study of annihilators in C*-algebras, showing that they are, in many ways, the best C*-algebra analogs of projections in von Neumann algebras. Using them, we obtain a type decomposition for arbitrary C*-algebras that is symmetric and completely consistent with the classical von Neumann algebra type decomposition. We also show that annihilators admit a very simple notion of equivalence that is again completely consistent with the notion of Murray-von Neumann equivalence in von Neumann algebras, sharing many of its general order theoretic properties.

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Tristan Bice. 2013-10-17. Annihilators and Type Decomposition in C*-Algebras. https://arxiv.org/abs/1310.4639

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