Locally Minimal Projections
Operator Algebras
2007-05-23 v1
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.
Cite
@article{arxiv.math/0008001,
title = {Locally Minimal Projections},
author = {Charles A. Akemann and Joel Anderson},
journal= {arXiv preprint arXiv:math/0008001},
year = {2007}
}
Comments
12 pages, AMS TeX