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 $A$-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.
