Jones, Frank2016-04-222016-04-221965Bagby, 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>.https://hdl.handle.net/1911/89788One 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.35 ppengCopyright 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.ThesisRICE0820reformatted digitalThesis Math. 1965 Bagby