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Let x and y be linearly independent unit vectors in our Hilbert space and P and Q the projections onto the subspaces they generate.
To prove this 'No Go' theorem, Kochen and Specker needed 117 rays in a three-dimensional Hilbert space.
S(H), the set of closed subspaces of a Hilbert space H, and
ii) There are vectors x(s), y(t) in a Hilbert space such that [Mathematical Expressions Omitted]
Roger Penrose's The Emperor's New Mind (Oxford University Press, 1989) provides the basis for this when he describes single points in phase and Hilbert space as follows: "A single point of phase space would be used to represent the (classical) state of an entire physical system.
Let C be a nonempty, closed, and convex subset of a real Hilbert space H.
In this paper, we construct a dissipative q-difference operator in the Hilbert space [L.
k]) with respect to the Hilbert space norm [[parallel]x[parallel].
Assume [pi] is a unitary representation of G into the unitary group of a separable Hilbert space H and assume that [pi]|[GAMMA] is a multiple of the left regular representation [[lambda].
Furthermore, a self-consistent definition of density is also required for a construction the Hilbert space where density is used for defining its inner product.
She covers normed spaces and operators, Frechet spaces and Banach theorems, duality, weak topologies, distributions, the Fourier transform and Sobolev spaces, Banach algebras, and unbounded operators in a Hilbert space.
is a Hilbert Space of function analytic in the unit disk with the inner product [<f,g>.
Louis De Brange [2] investigated properties of the Hilbert space of entire functions.