In the Amemiya-Ando problem 3 is enough

2012/08/04 by Adam Paszkiewicz, Paszkiewicz, Adam
Computer Science · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #math.FA

paper · pdf · doi:10.48550/arxiv.1208.0905

arxiv created 2012/08/04 · openalex publication_date 2012/08/04 · arxiv updated 2012/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In any infinite dimensional Hilbert space \mathcal H there exist orthogonal projections Q₁, Q₂ and Q₃, such that a sequence (P_n... P₁(x)) diverges in norm for some P₁,P₂,...∈\Q₁,Q₂,Q₃\ and x∈\mathcal H.

Related

• The Amemiya-Ando conjecture falls
• Strange products of projections
• The norm attainment problem for functions of projections
• Orthogonality in normed spaces
• The Method of Alternating Projections