Products of orthogonal projections and polar decompositions

2010/11/23 by Gustavo Corach, Corach, Gustavo, Alejandra Maestripieri +1 · 2 citations
Mathematics · #47A05 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:47A05

paper · pdf · doi:10.48550/arxiv.1011.5237

arxiv created 2010/11/23 · arxiv updated 2010/11/25

Abstract

We characterize the sets \XX of all products PQ, and \YY of all products PQP, where P,Q run over all orthogonal projections and we solve the problems argmin\‖P-Q‖: (P,Q) ∈ \cal Z\, for \cal Z=\XX or \YY. We also determine the polar decompositions and Moore-Penrose pseudoinverses of elements of \XX.

Cited by

• The block matrix representations for the quasi-projection pairs on Hilbert C^*-modules
• Factorizations of linear relations by idempotents

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