IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
Weighted Procrustes problems
Autor/es:
MAXIMILIANO CONTINO; ALEJANDRA MAESTRIPIERI; JUAN IGNACIO GIRIBET
Revista:
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Editorial:
ACADEMIC PRESS INC ELSEVIER SCIENCE
Referencias:
Lugar: Amsterdam; Año: 2017 vol. 445 p. 443 - 443
ISSN:
0022-247X
Resumen:
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).