Positive combinations of projections in von Neumann algebras and purely infinite simple C*-algebras

Details Positive combinations of projections in von Neumann algebras and purely infinite simple C*-algebras Positive combinations of projections in von Neumann algebras and purely infinite simple C*-algebras

2012-01-23

arxiv.org/abs/1201.4844v1

Science China Mathematics, 54, No. 2 (2011) 1-10

Mathematics

Operator Algebras

Scientific paper

We give an overview of the question: which positive elements in an operator algebra can be written as a linear combination of projections with positive coefficients. A special case of independent interest is the question of which positive elements can be written as a sum of finitely many projections. We focus on von Neumann algebras, on purely infinite simple C*-algebras, and on their associated multiplier algebras.

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