A canonical decomposition for linear operators and linear relations
Functional Analysis
2007-05-23 v1 Mathematical Physics
math.MP
Abstract
An arbitrary linear relation (multivalued operator) acting from one Hilbert space to another Hilbert space is shown to be the sum of a closable operator and a singular relation whose closure is the Cartesian product of closed subspaces. This decomposition can be seen as an analog of the Lebesgue decomposition of a measure into a regular part and a singular part. The two parts of a relation are characterized metrically and in terms of Stone's characteristic projection onto the closure of the linear relation.
Cite
@article{arxiv.math/0611045,
title = {A canonical decomposition for linear operators and linear relations},
author = {S. Hassi and Z. Sebestyén and H. S. V. de Snoo and F. H. Szafraniec},
journal= {arXiv preprint arXiv:math/0611045},
year = {2007}
}
Comments
to appear in Acta Math. Hungarica, volume 116(1-2)