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Noun

Hilbert space - a metric space that is linear and complete and (usually) infinite-dimensional

metric 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

Mentioned in

metric space

References in periodicals archive

where C is a nonempty closed convex subset of a real Hilbert space H and f : H x H [right arrow] R is a given bifunction with f (x,x) = 0 for all x [member of] C.

Strong Convergence of a New Hybrid Algorithm for Fixed Point Problems and Equilibrium Problems

Progress in brain research indicates (Roy and Kafatos, 1999, 2003, 2004) that to apply the wave function formalism used in quantum mechanics, it is necessary to consider relevant Hilbert space structure.

GEOMETRONEURODYNAMICS AND NEUROSCIENCE

Let H be a real Hilbert space with inner product [??]*,* [??] and norm [parallel] * [parallel], respectively.

The modified extragradient method for nonexpansive multivalued mappings and variational inequality problems

A frame for a Hilbert space firstly emerged in the work on nonharmonic Fourier series owing to Duffin and Schaeffer [1], which has made great contributions to various fields because of its nice properties; the reader can examine the papers [2-12] for background and details of frames.

A New Inequality for Frames in Hilbert Spaces

In virtually any representation of quantum theory, the states can be perceived as constructed in a suitable user-friendly Hilbert space H.

Hermitian-Non-Hermitian Interfaces in Quantum Theory

In the mathematical framework of information theory, density operators (quantum states) are positive operators with trace 1 on complex separable Hilbert space H, and the set of all density operators is denoted by S(H) on H.

Preservers for the Tsallis Entropy of Convex Combinations of Density Operators

Throughout this paper, we always assume that C be a closed convex subset of a real Hilbert space H with inner product and norm are denoted by <*,*> and [parallel]*[parallel], respectively.

On Solving of Constrained Convex Minimize Problem Using Gradient Projection Method

[6] considered an implicit Volterra difference equation in a Hilbert space and obtained sufficient conditions so that the solutions exist and have a bounded behavior.

Stability for Linear Volterra Difference Equations in Banach Spaces

(On the other hand, if a Banach space is a CAT([kappa]) space for some [kappa] [member of] R, then it is necessarily a Hilbert space and CAT(0).) For a thorough discussion of these spaces and of the fundamental role they play in geometry, see Bridson and Haefliger [2].

Generalized CAT(0) spaces

A Hilbert space over the complex field is denoted, in [6], as H.The standard definition of a norm on an inner product space, including on a Hilbert space, is

On Some Inequalities with Operators in Hilbert Spaces