Strong sums of projections in von Neumann factors
Operator Algebras
2008-11-19 v1 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.0811.2835,
title = {Strong sums of projections in von Neumann factors},
author = {Victor Kaftal and Ping Wong Ng and Shuang Zhang},
journal= {arXiv preprint arXiv:0811.2835},
year = {2008}
}