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.

The de Branges space associated with E is a

Hilbert space B(E) of entire functions such that (i) [f|.

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.