A canonical decomposition for linear operators and linear relations

2006/11/02 by S. Hassi, Z. Sebestyén, Hassi, S. +5
Mathematics · Physics and Astronomy · #47A05 #47A06 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #math-ph #math.FA #math.MP #msc:47A05 #msc:47A06

paper · pdf · doi:10.48550/arxiv.math/0611045

to appear in Acta Math. Hungarica, volume 116(1-2)

arxiv created 2006/11/02 · arxiv updated 2009/12/01

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.

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