Consider a renormalized density matrix . The eigenvalues of lie in the interval . If this matrix were a finite matrix we could use the triangle inequality to show that
For infinite-size matrices the trace is usually infinite so that a regularization is needed. Suppose that is the regularization parameter and is the regularized trace. Then an analytic function, which is bounded in the region and which satisfies condition (19), vanishes identically. Thus, we conclude that and there is only one analytic continuation to non-integer , namely the one given by function .
Living Rev. Relativity 14, (2011), 8
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