Some inequalities for the triangle.
Weighted projections into closed subspaces
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.
Sard's approximation processes and oblique projections
Three problems arising in approximation theory are studied. These problems have already been studied by Arthur Sard. The main goal of this paper is to use geometrical compatibility theory to extend Sard's results and get characterizations of the sets of solutions.
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