IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
Approximation by Partial Isometries and Symmetric Approximation of Finite Frames
Autor/es:
ANTEZANA, JORGE; CHIUMIENTO, EDUARDO
Revista:
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
Editorial:
BIRKHAUSER BOSTON INC
Referencias:
Año: 2017 p. 1 - 1
ISSN:
1069-5869
Resumen:
We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize all the solutions. In particular, this allows us to give a simple necessary and sufficient condition for uniqueness. We then apply these results to solve the global problem of approximation by partial isometries, and to extend the notion of symmetric approximation of frames introduced in Frank et al. (Trans Am Math Soc 354: 777?793, 2002). In addition, we characterize symmetric approximations of frames belonging to a prescribed subspace.