Locally Minimal Projections
Abstract
Given an n-tuple a1, ..., an 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, pajp is a scalar multiple of p. Assuming that a1, ...,an, 1 is a linearly independent set in the Calkin algebra, then p can be chosen of infinite rank.
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