Weighted projections into closed subspaces
Volume 216 / 2013
Studia Mathematica 216 (2013), 131-148
MSC: Primary 47A07; Secondary 47A58.
DOI: 10.4064/sm216-2-3
Abstract
We study -projections, i.e. operators on a Hilbert space \mathcal {H} which act as projections when a seminorm is considered in \mathcal {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 \mathcal {H}. We also study the relationship between weighted least squares problems and compatibility.