We study A-projections, i.e. operators on a Hilbert space 𝓗 which act as projections when a seminorm is considered in 𝓗. The A-projections were introduced by Mitra and Rao (1974) for finite-dimensional spaces. We relate this concept to the theory of compatibility between positive operators and closed subspaces of 𝓗. We also study the relationship between weighted least squares problems and compatibility.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm216-2-3,
author = {G. Corach and G. Fongi and A. Maestripieri},
title = {Weighted projections into closed subspaces},
journal = {Studia Mathematica},
volume = {215},
year = {2013},
pages = {131-148},
zbl = {1339.47003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm216-2-3}
}
G. Corach; G. Fongi; A. Maestripieri. Weighted projections into closed subspaces. Studia Mathematica, Tome 215 (2013) pp. 131-148. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm216-2-3/