Sums of equivalent sequences of positive operators in von Neumann factors

Catalin Dragan; Victor Kaftal

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arXiv · 1504.03193

Sums of equivalent sequences of positive operators in von Neumann factors

Catalin Dragan·Victor Kaftal

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Abstract

Let A be a positive operator in an infinite sigma-finite von Neumann factor M and let B_j be a sequence of positive elements in M. We give sufficient conditions for decomposing A into a sum of elements C_j equivalent to B_j for all j ( C equivalent to B in M means that C=XX* and B=X*X for some X in M) and when C_j are unitarily equivalent to B_j for all j. This extends recent work of Bourin and Lee for the case of B_j= B for all j and M=B(H) and answers affirmatively their conjecture. For the case when B_j= B for all j we provide necessary conditions, which in the type III case are also sufficient.

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BibTeX RIS

Catalin Dragan, Victor Kaftal. 2015-04-13. Sums of equivalent sequences of positive operators in von Neumann factors. https://arxiv.org/abs/1504.03193

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