Weighted Procrustes problems. Contino, M., Giribet, J. I., & Maestripieri, A. Journal of Mathematical Analysis and Applications, 445(1):443–458, 2017. doi abstract bibtex Let H be a Hilbert space, L(H) the algebra of bounded linear operators on H and W???L(H) a positive operator such that W1/2 is in the p-Schatten class, for some 1???p\textless???. Given A???L(H) with closed range and B???L(H), we study the following weighted approximation problem: analyze the existence ofminX???L(H)???AX???B???p,W where ???X???p,W=???W1/2X???p. In this paper we prove that the existence of this minimum is equivalent to a compatibility condition between R(B) and R(A) involving the weight W, and we characterize the operators which minimize this problem as W-inverses of A in R(B).
@Article{Contino2017,
author = {Contino, Maximiliano and Giribet, Juan Ignacio and Maestripieri, Alejandra},
title = {{Weighted Procrustes problems}},
journal = {Journal of Mathematical Analysis and Applications},
year = {2017},
volume = {445},
number = {1},
pages = {443--458},
issn = {10960813},
abstract = {Let H be a Hilbert space, L(H) the algebra of bounded linear operators on H and W???L(H) a positive operator such that W1/2 is in the p-Schatten class, for some 1???p{\textless}???. Given A???L(H) with closed range and B???L(H), we study the following weighted approximation problem: analyze the existence ofminX???L(H)???AX???B???p,W where ???X???p,W=???W1/2X???p. In this paper we prove that the existence of this minimum is equivalent to a compatibility condition between R(B) and R(A) involving the weight W, and we characterize the operators which minimize this problem as W-inverses of A in R(B).},
doi = {10.1016/j.jmaa.2016.07.050},
file = {:Users/juan/Library/Application Support/Mendeley Desktop/Downloaded/Contino, Giribet, Maestripieri - 2017 - Weighted Procrustes problems.pdf:pdf},
keywords = {Oblique projections,Operator approximation,Schatten p classes},
}
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