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  • 1 University of Vaasa Department of Mathematics and Statistics P.O. Box 700 65101 Vaasa Finland P.O. Box 700 65101 Vaasa Finland
  • 2 Eötvös Loránd University Department of Applied Analysis Pázmány Péter sétány 1/C 1117 Budapest Hungary Pázmány Péter sétány 1/C 1117 Budapest Hungary
  • 3 University of Groningen Department of Mathematics and Computing Science P.O. Box 800 9700 AV Groningen Nederland P.O. Box 800 9700 AV Groningen Nederland
  • 4 Uniwersytet Jagielloński Institute of Mathematics ul. Reymonta 4 30059 Kraków Poland ul. Reymonta 4 30059 Kraków Poland
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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.