An elementary proof of the spectral theorem for unbounded operators

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dc.contributor.advisorJones, Franken_US
dc.creatorBagby, Richard Julianen_US
dc.date.accessioned2016-04-22T21:58:31Zen_US
dc.date.available2016-04-22T21:58:31Zen_US
dc.date.issued1965en_US
dc.description.abstractOne of the proofs of the spectral theorem for bounded operators begins by proving that a bounded, positive definite self-adjoint operator on a Hilbert space has a unique positive definite self-adjoint square root. From this result, I will show directly that an unbounded positive definite selfadjoint operator also has a unique square root. From this, I will derive the spectral theorem for unbounded self-adjoint operators. With this approach, the necessary results follow directly from elementary properties of operators on a Hilbert space. The resolution of the identity corresponding to an operator is obtained directly from the operator, rather than from the spectral resolution of related operators.en_US
dc.format.digitalOriginreformatted digitalen_US
dc.format.extent35 ppen_US
dc.identifier.callnoThesis Math. 1965 Bagbyen_US
dc.identifier.citationBagby, Richard Julian. "An elementary proof of the spectral theorem for unbounded operators." (1965) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/89788">https://hdl.handle.net/1911/89788</a>.en_US
dc.identifier.digitalRICE0820en_US
dc.identifier.urihttps://hdl.handle.net/1911/89788en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.titleAn elementary proof of the spectral theorem for unbounded operatorsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematicsen_US
thesis.degree.disciplineNatural Sciencesen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Artsen_US
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