An operator on a separable Hilbert space with all polynomials hypercyclic

Operator Extensions on Hilbert Space

Locating the Range of an Operator on a Hilbert Space

exists (is computable) for each x in H; if P is that projection, / is the identity operator on H, and the adjoint T*ofT exists, then / P is the projection of H on ker(3*), the kernel of T*. (For an example to show that the existence of the adjoint of a bounded operator on a Hilbert space is not automatic in constructive mathematics, see Brouwerian Example 3 in [7]; see also Example 2 below.) Th...

OPERATOR THEORY ON HILBERT SPACE Class notes

Operator Preconditioning in Hilbert Space

2010 1 Introduction The numerical solution of linear elliptic partial differential equations consists of two main steps: discretization and iteration, where generally some conjugate gradient method is used for solving the finite element discretization of the problem. However, when for elliptic problems the dis-cretization parameter tends to zero, the required number of iterations for a prescrib...

Separable Hilbert space in Loop Quantum Gravity

We study the separability of the state space of loop quantum gravity. In the standard construction, the kinematical Hilbert space of the diffeomorphism-invariant states is nonseparable. This is a consequence of the fact that the knot-space of the equivalence classes of graphs under diffeomorphisms is noncountable. However, the continuous moduli labeling these classes do not appear to affect the...