# Hilbert space

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Related to Hilbert space: vector space, Banach space
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 Noun 1 Hilbert space - a metric space that is linear and complete and (usually) infinite-dimensionalmetric space - a set of points such that for every pair of points there is a nonnegative real number called their distance that is symmetric and satisfies the triangle inequality
Translations
HilbertraumHilbert-Raum
Hilbertin avaruus
espace de Hilbert
Hilbert-tér
spazio di Hilbertspazio hilbertiano
ヒルベルト空間
Hilbertrum
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References in periodicals archive ?
1999), explicit formulas are given for P [conjunction] Q in terms of P and Q when the Hilbert space is finite dimensional so the formula for [delta] can be made more explicit in this case.
Quantum states are elements of Hilbert space; quantum observables are Hilbert space operators.
But most important is the representation of quantum events (or propositions) with closed subspaces of Hilbert spaces: if we let "A" denote some observable, "[delta]" denote some Borel set of real numbers that can be values of A, and "(A,[delta])" denote the quantum event of a measurement of A yielding a value in A (or equivalently, the proposition which asserts that this event has occurred, or perhaps, will occur) then we can represent (A,[delta]) with the closed subspace CS(A,[delta]) of the Hilbert space H in which A is represented, where CS(A,[delta]) is defined as follows: a vector v of H is in CS(A,[delta]) iff there is a probability of I that a measurement of A, for a quantum system in the state represented by v, will yield a value in [delta].
v) There is a constant C such that for any Hilbert space H and for any finitely supported function a : G [right arrow] B(H) we have
Within the plasmic folds of a kind of supercoordinate Hilbert space, Wallace choreographs a dance of distentions (not all of which appear as characters) that are for purposes of the dance indistinguishable from the envelope of fatality with whose topological surface they interface and from whose curvature and parallax they fail to deduce their imprisonment in a paint-by-number Las Meninas that seems drawn to scale by the Logico-Tractator himself.
Among his topics are representations of solutions to operator equations, bounds for condition numbers of diagonalizable matrices, functions of a compact operator in a Hilbert space, regular functions of a bounded non-self-adjoint operator, and commutators and perturbations of operator functions.
2) We will exploit spin-orbit quantum correlations generated within single photons and/or among few correlated photons to demonstrate novel quantum-information protocols using both the polarization and the transverse modes to encode and manipulate multiple qubits in each photon and for the implementation of quantum simulations of material systems based on photonic quantum walks in the Hilbert space of the light transverse modes.
Let H be an infinite dimensional separable Hilbert space of analytic functions defined in D = {z [member of] C, [absolute value of (z)] < 1} such that, for each [lambda] [member of] D, the linear functional of point evaluation [e.
Let C be a nonempty closed convex subset of a real Hilbert space H and let T : C [right arrow] H be a [alpha]-inverse strongly monotone and let r > 0 be a constant.
Eryilmaz [6] studied q-Sturm-Liouville boundary value problem in the Hilbert space with a spectral parameter in the boundary condition and he proved theorems on the completeness of the system of eigenvalues and eigenvectors of operator by Pavlov's method.
This condition is valid in every Hilbert space, but also in some Banach spaces, e.

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