spectral theorem

Target entity: spectral theorem
Context triple: [Stone’s theorem on one-parameter unitary groups, relatedTo, spectral theorem]

• A. Naimark dilation theorem
  The Naimark dilation theorem is a fundamental result in operator theory and quantum measurement theory stating that every positive operator-valued measure can be realized as the compression of a projection-valued measure on a larger Hilbert space.
• B. Courant–Fischer min–max theorem
  The Courant–Fischer min–max theorem is a fundamental result in linear algebra and spectral theory that characterizes the eigenvalues of a Hermitian (or symmetric) matrix via variational min–max principles over subspaces.
• C. Gelfand–Naimark theorem
  The Gelfand–Naimark theorem is a foundational result in functional analysis that characterizes C*-algebras as algebras of bounded operators on a Hilbert space (and, in the commutative case, as algebras of continuous functions on a locally compact Hausdorff space).
• D. Introduction to Hilbert Space and the Theory of Spectral Multiplicity
  "Introduction to Hilbert Space and the Theory of Spectral Multiplicity" is a classic mathematical text by Paul Halmos that provides a foundational treatment of Hilbert space theory and the spectral analysis of linear operators.
• E. Bohr–Courant theorem
  The Bohr–Courant theorem is a classical result in analytic number theory describing the value distribution of Dirichlet series, particularly the Riemann zeta function, and serves as a precursor to modern universality theorems such as Voronin’s.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: spectral theorem
Target entity description: The spectral theorem is a fundamental result in functional analysis that characterizes normal (including self-adjoint) operators on Hilbert spaces via their decomposition into integrals over their spectra, enabling a powerful generalization of diagonalization.

• A. Naimark dilation theorem
  The Naimark dilation theorem is a fundamental result in operator theory and quantum measurement theory stating that every positive operator-valued measure can be realized as the compression of a projection-valued measure on a larger Hilbert space.
• B. Courant–Fischer min–max theorem
  The Courant–Fischer min–max theorem is a fundamental result in linear algebra and spectral theory that characterizes the eigenvalues of a Hermitian (or symmetric) matrix via variational min–max principles over subspaces.
• C. Gelfand–Naimark theorem
  The Gelfand–Naimark theorem is a foundational result in functional analysis that characterizes C*-algebras as algebras of bounded operators on a Hilbert space (and, in the commutative case, as algebras of continuous functions on a locally compact Hausdorff space).
• D. Introduction to Hilbert Space and the Theory of Spectral Multiplicity
  "Introduction to Hilbert Space and the Theory of Spectral Multiplicity" is a classic mathematical text by Paul Halmos that provides a foundational treatment of Hilbert space theory and the spectral analysis of linear operators.
• E. Bohr–Courant theorem
  The Bohr–Courant theorem is a classical result in analytic number theory describing the value distribution of Dirichlet series, particularly the Riemann zeta function, and serves as a precursor to modern universality theorems such as Voronin’s.
• F. None of above. chosen