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arXiv:math/0611045 [math.FA]AbstractReferencesReviewsResources

A canonical decomposition for linear operators and linear relations

S. Hassi, Z. Sebestyén, H. S. V. de Snoo, F. H. Szafraniec

Published 2006-11-02Version 1

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.

Comments: to appear in Acta Math. Hungarica, volume 116(1-2)
Categories: math.FA, math-ph, math.MP
Subjects: 47A05, 47A06
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