mathematics, the Hilbert projection theorem is a famous result of convex analysis that says that for every vector x {\displaystyle x} in a Hilbert space H {\displaystyle...

parallelogram law implies that any Hilbert space is a uniformly convex Banach space. This subsection employs the Hilbert projection theorem. If C is a non-empty closed...

{\displaystyle V} is a Hilbert space, the concept of orthogonality can be used. A projection P {\displaystyle P} on a Hilbert space V {\displaystyle V}...

which the spectral theorem applies are self-adjoint operators or more generally normal operators on Hilbert spaces. The spectral theorem also provides a...

the given Hilbert space. Projection-valued measures are used to express results in spectral theory, such as the important spectral theorem for self-adjoint...

{\displaystyle H.} The Hilbert projection theorem guarantees that for any nonempty closed convex subset C {\displaystyle C} of a Hilbert space there exists...

Hilbert number Hilbert plane Hilbert polynomial Hilbert series Hilbert ring Hilbert–Samuel function Hilbert projection theorem Hilbert R-tree Hilbert...

applying the Born rule to some density operator. Gleason's theorem holds if the dimension of the Hilbert space is 3 or greater; counterexamples exist for dimension...

(Y))} is a closed subspace of the Hilbert space L 2 ( Ω ) {\displaystyle L^{2}(\Omega )} . By the Hilbert projection theorem, the necessary and sufficient...

theory) Hilbert projection theorem (convex analysis) Hille–Yosida theorem (functional analysis) Hindman's theorem (Ramsey theory) Hinge theorem (geometry)...