Nonseparability and von Neumann's theorem for domains of unbounded operators

Show simple item record ter Elst, Antonius en Sauter, M en 2016-08-23T04:48:15Z en 2016 en
dc.identifier.citation Journal of Operator Theory, 2016, 75 (2), pp. 367 - 386 en
dc.identifier.issn 0379-4024 en
dc.identifier.uri en
dc.description.abstract A classical theorem of von Neumann asserts that every unbounded self-adjoint operator $A$ in a \textit{separable} Hilbert space is unitarily equivalent to an operator $B$ such that $D(A)\cap D(B)=\{0\}$. Equivalently this can be formulated as a property for nonclosed operator ranges. We will show that von Neumann's theorem does not directly extend to the nonseparable case. In this paper we prove a characterisation of the property that an operator range $\cR$ in a general Hilbert space admits a unitary operator $U$ such that $U\mathcal{R}\cap\mathcal{R}=\{0\}$. This allows us to study stability properties of operator ranges with the aforementioned property. en
dc.description.uri en
dc.language English en
dc.publisher Theta Foundation en
dc.relation.ispartofseries Journal of Operator Theory en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. Details obtained from en
dc.rights.uri en
dc.title Nonseparability and von Neumann's theorem for domains of unbounded operators en
dc.type Journal Article en
dc.identifier.doi 10.7900/jot.2015apr29.2073 en
pubs.issue 2 en
pubs.begin-page 367 en
pubs.volume 75 en
dc.description.version VoR - Version of Record en en
pubs.end-page 386 en
pubs.publication-status Published en
dc.rights.accessrights en
pubs.subtype Article en
pubs.elements-id 506111 en Science en Mathematics en
dc.identifier.eissn 1841-7744 en
pubs.record-created-at-source-date 2015-11-24 en

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