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

 dc.contributor.author ter Elst, Antonius en dc.contributor.author Sauter, M en dc.date.accessioned 2016-08-23T04:48:15Z en dc.date.issued 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 http://hdl.handle.net/2292/30117 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 http://arxiv.org/abs/1504.07790 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 http://www.mathjournals.org/jot/ en dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm 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 pubs.author-url http://www.mathjournals.org.ezproxy.auckland.ac.nz/jot/2016-075-002/2016-075-002-006.html en pubs.end-page 386 en pubs.publication-status Published en dc.rights.accessrights http://purl.org/eprint/accessRights/RestrictedAccess en pubs.subtype Article en pubs.elements-id 506111 en pubs.org-id Science en pubs.org-id Mathematics en dc.identifier.eissn 1841-7744 en pubs.record-created-at-source-date 2015-11-24 en
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