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- W2488290411 abstract "Let $mathcal{H}$ be a Hilbert space, $L(mathcal{H})$ the algebra of bounded linear operators on $mathcal{H}$ and $W in L(mathcal{H})$ a positive operator such that $W^{1/2}$ is in the p-Schatten class, for some $1 leq p< infty.$ Given $A in L(mathcal{H})$ with closed range and $B in L(mathcal{H}),$ we study the following weighted approximation problem: analize the existence of $$underset{X in L(mathcal{H})}{min}Vert AX-B Vert_{p,W},$$ where $Vert X Vert_{p,W}=Vert W^{1/2}X Vert_{p}.$ 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 $R(B).$" @default.
- W2488290411 created "2016-08-23" @default.
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- W2488290411 date "2017-01-01" @default.
- W2488290411 modified "2023-10-16" @default.
- W2488290411 title "Weighted Procrustes problems" @default.
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- W2488290411 doi "https://doi.org/10.1016/j.jmaa.2016.07.050" @default.
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