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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.

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Periodica Mathematica Hungarica
Authors: Z. Sebestyén, L. Lempert, V. Komornik, T. Szilágyi and T. Szőnyi
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Periodica Mathematica Hungarica
Authors: A. Lee, I. Bihari, M. Farkas, Gy. Terdik, R. Wiegandt, Z. Sebestyén, J. Lehel and V. Totik
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