Projections in operator ranges

2005/09/14 by Gustavo Corach, Corach, Gustavo, Alejandra Maestripieri +3
Computer Science · Mathematics · Physics and Astronomy · #46C05 #46C07 #47A62 #Electromagnetic Scattering and Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Numerical methods in inverse problems #math.FA #msc:46C05 #msc:46C07 #msc:47A62

paper · pdf · doi:10.48550/arxiv.math/0509330

arxiv created 2005/09/14 · openalex publication_date 2005/09/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If \H is a Hilbert space, A is a positive bounded linear operator on \cH and \cS is a closed subspace of \cH, the relative position between \cS and A^-1(\cS \orto) establishes a notion of compatibility. We show that the compatibility of (A,\cS) is equivalent to the existence of a convenient orthogonal projection in the operator range R(A^1/2) with its canonical Hilbertian structure.

Related

• Weighted projections into closed subspaces
• Operators with compatible ranges
• Hilbert space operators with compatible off-diagonal corners
• Weighted projections and Riesz frames
• Proper subspaces and compatibility