Locally Minimal Projections

2000/07/31 by Charles A. Akemann, Joel Anderson, Akemann, Charles A. +1
Computer Science · Engineering · Mathematics · #15A99 (Secondary) #47A13 (Primary) #Advanced Mathematical Modeling in Engineering #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:15A99 #msc:47A13

paper · pdf · doi:10.48550/arxiv.math/0008001

12 pages, AMS TeX

arxiv created 2000/07/31 · openalex publication_date 2000/07/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given an n-tuple a₁, ..., 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 a₁, ...,a_n, 1 is a linearly independent set in the Calkin algebra, then p can be chosen of infinite rank.

Related

• Weighted projections into closed subspaces
• Wigner's type theorem in terms of linear operators which send\n projections of a fixed rank to projections of other fixed rank
• Sums of compositions of pairs of projections
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• Linear preservers of rank k projections