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Locally Minimal Projections

Charles A. Akemann·Joel Anderson
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Abstract

Given an n-tuple {a_1, ..., a_n} of self-adjoint operators on an infinite dimensional Hilbert space H and a positive integer k, there exists a projection p of rank k such that, for each for j = 1, ..., n, pa_jp is a scalar multiple of p. Assuming that {a_1, ...,a_n, 1} is a linearly independent set in the Calkin algebra, then p can be chosen of infinite rank.

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Charles A. Akemann, Joel Anderson. 2000-07-31. Locally Minimal Projections. https://arxiv.org/abs/math/0008001

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