Strong sums of projections in von Neumann factors

Details Strong sums of projections in von Neumann factors Strong sums of projections in von Neumann factors

2008-11-18

arxiv.org/abs/0811.2835v1

Mathematics

Operator Algebras

Scientific paper

This paper presents necessary and sufficient conditions for a positive bounded operator on a separable Hilbert space to be the sum of a finite or infinite collection of projections (not necessarily mutually orthogonal), with the sum converging in the strong operator topology if the collection is infinite. A similar necessary condition is given when the operator and the projections are taken in a type II von Neumann factor, and the condition is proven to be also sufficient if the operator is "diagonalizable". A simpler necessary and sufficient condition is given in the type III factor case.

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