English

Products of orthogonal projections and polar decompositions

Functional Analysis 2010-11-25 v1

Abstract

We characterize the sets \XX\XX of all products PQPQ, and \YY\YY of all products PQPPQP, where P,QP,Q run over all orthogonal projections and we solve the problems argmin{PQ:(P,Q)Z}\arg\min\{\|P-Q\|: (P,Q) \in \cal Z\}, for Z=\XX\cal Z=\XX or \YY.\YY. We also determine the polar decompositions and Moore-Penrose pseudoinverses of elements of \XX.\XX.

Keywords

Cite

@article{arxiv.1011.5237,
  title  = {Products of orthogonal projections and polar decompositions},
  author = {Gustavo Corach and Alejandra Maestripieri},
  journal= {arXiv preprint arXiv:1011.5237},
  year   = {2010}
}