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arXiv math/00080012000-08math.OA

局部极小投影

Locally Minimal Projections

Charles A. Akemann, Joel Anderson

备注：: 12 pages, AMS TeX

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摘要：

给定n元组{a_1，...，a_n}的自伴算子在无穷维希尔伯特空间H和一个正整数k上，存在秩为k的投影p，使得对于每个j = 1，.，n，pa_jp是p的标量倍数。假设{a_1，...，a_n，1}是Calkin代数中的一个线性无关集，则p可以取无限秩.

英文摘要：

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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