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dc.contributor.authorĐorđević, Bogdanen_US
dc.date.accessioned2021-09-20T10:41:02Z-
dc.date.available2021-09-20T10:41:02Z-
dc.date.issued2021-12-01-
dc.identifier.issn1664-2368-
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/4655-
dc.description.abstractLet A be a closed operator on a separable Hilbert space H. In this paper we obtain sufficient conditions for the existence of a solution to the Lyapunov operator equation A∗X+ X∗A= I, under the assumption that it is singular (without a unique solution). Specially, if A is a self-adjoint operator, we derive sufficient conditions for the solution X to be symmetric. We also show that these results hold in the bounded-operator setting and in C∗- algebras. By doing so, we generalize some known results regarding solvability conditions for algebraic equations in C∗- algebras. We apply our results to study some functional problems in abstract analysis.en_US
dc.publisherSpringer Linken_US
dc.relation.ispartofAnalysis and Mathematical Physicsen_US
dc.subjectAbstract Cauchy problems | Equations in C - algebras ∗ | Fréchet derivative | Lyapunov operator equationsen_US
dc.titleSingular Lyapunov operator equations: applications to C∗- algebras, Fréchet derivatives and abstract Cauchy problemsen_US
dc.typeArticleen_US
dc.identifier.doi10.1007/s13324-021-00596-z-
dc.identifier.scopus2-s2.0-85114421903-
dc.contributor.affiliationMathematicsen_US
dc.contributor.affiliationMathematical Institute of the Serbian Academy of Sciences and Arts-
dc.relation.firstpage160-
dc.relation.issue4-
dc.relation.volume11-
dc.description.rank~M21a-
item.openairetypeArticle-
item.cerifentitytypePublications-
item.fulltextNo Fulltext-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.grantfulltextnone-
crisitem.author.orcid0000-0002-6751-6867-
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