Weighted Procrustes problems

MAXIMILIANO CONTINO; MAXIMILIANO CONTINO; ALEJANDRA MAESTRIPIERI; ALEJANDRA MAESTRIPIERI; JUAN IGNACIO GIRIBET; JUAN IGNACIO GIRIBET

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2017 vol. 445 p. 443 - 458

0022-247X

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 W^{1/2} is in the p-Schatten class, for some 1 ≤ p < ∞. Given A ∈ L(H) with closed range and B ∈ L(H), we study the following weighted approximation problem: analize the existence ofmin ||AX−B||p,W, X ∈L(H)where ||X||p,W =||W^{1/2} X ||p.In this paper we prove that the existence of this minimum is equivalent to a compatibility conditionbetween 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).