Lebesgue type decompositions for linear relations and Ando’s uniqueness criterion

Hassi, Seppo and Sebestyén, Zoltán and Snoo, Henk de: Lebesgue type decompositions for linear relations and Ando’s uniqueness criterion. Acta scientiarum mathematicarum, (84) 3-4. pp. 465-507. (2018)

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Abstract

A linear relation, i.e., a multivalued operator T from a Hilbert space H to a Hilbert space K has Lebesgue type decompositions T = T1 + T2, where T1 is a closable operator and T2 is an operator or relation which is singular. There is one canonical decomposition, called the Lebesgue decomposition of T, whose closable part is characterized by its maximality among all closable parts in the sense of domination. All Lebesgue type decompositions are parametrized, which also leads to necessary and sufficient conditions for the uniqueness of such decompositions. Similar results are given for weak Lebesgue type decompositions, where T1 is just an operator without being necessarily closable. Moreover, closability is characterized in different useful ways. In the special case of range space relations the above decompositions may be applied when dealing with pairs of (nonnegative) bounded operators and nonnegative forms as well as in the classical framework of positive measures.

Item Type: Article
Journal or Publication Title: Acta scientiarum mathematicarum
Date: 2018
Volume: 84
Number: 3-4
Page Range: pp. 465-507
ISSN: 0001-6969
DOI: https://doi.org/10.14232/actasm-018-757-0
Uncontrolled Keywords: Matematika
Additional Information: Bibliogr.: p. 505-507. ; összefoglalás angol nyelven
Official URL: http://www.acta.hu
Date Deposited: 2019. Jan. 30. 05:40
Last Modified: 2019. Sep. 09. 13:44
URI: http://acta.bibl.u-szeged.hu/id/eprint/56926

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