Linked from

The 68 pages that link to Hilbert space, each with the reason it gives.

• Pascual JordanRelated: Quantum mechanics uses this structure to represent states and measurable quantities.

• Kirszbraun theoremNarrower topic: The theorem’s source and target spaces must have Hilbert geometry.

• QuantizationRelated: Its operators provide the mathematical setting for quantum observables and spectra.

• Wigner's theoremNarrower topic: The theorem's unitary and antiunitary operators act on this state space.

• Operator theoryRelated: Its geometry supports adjoints, orthogonality, and spectral results for operators.

• Peter–Weyl theoremNarrower topic: The square-integrable functions form a Hilbert space decomposed by the theorem.

• Symmetry in quantum mechanicsNarrower topic: Quantum symmetry operators act on the Hilbert space of states.

• Cardinality of the continuumNarrower topic: Common separable Hilbert spaces have continuum many vectors, linking functional analysis to 𝔠.

• Invariant subspace problemNarrower topic: The complex Hilbert-space setting is the narrower version that remains unresolved.

• Anna Johnson Pell WheelerRelated: Hilbert-space methods became central to the operator theory surrounding her research.

• Bra–ket notationNarrower topic: Kets represent vectors in the Hilbert space of a quantum system.

• Dvoretzky's theoremCompared with: Hilbert spaces are already Euclidean in every finite-dimensional subspace, unlike general normed spaces.

• Foundations of quantum mechanicsNarrower topic: Quantum states are represented by vectors or rays in Hilbert space.

• Hellinger–Toeplitz theoremNarrower topic: Completeness supplies the Banach-space setting needed for the closed graph theorem.

• Kosambi–Karhunen–Loève theoremRelated: Mean-square random variables form an inner-product setting for orthogonal expansions.

• Lions–Lax–Milgram theoremRelated: The classical theorem is stated for bounded forms on Hilbert spaces.

• Mathematical formulation of quantum mechanicsRelated: Quantum state vectors inhabit Hilbert spaces, where inner products determine transition amplitudes.

• Petr–Douglas–Neumann theoremNarrower topic: Inner products make adjoints and operator positivity available in the theorem.