hilbert space in a sentence

Examples

1. Not every wave function belongs to the Hilbert space, though.
2. Every finite-dimensional inner product space is also a Hilbert space.
3. Two prominent examples occur for Banach spaces and Hilbert spaces.
4. This language translates into convergence properties of Hilbert space operators.
5. Tensor products of Hilbert spaces arise often in quantum mechanics.
6. Banach spaces are a different generalization of Hilbert spaces.
7. This is justified rigorously by basic Hilbert space theory.
8. The Hilbert space describing such a system is two-dimensional.
9. For separable Hilbert spaces, it is the unique ideal.
10. For the finite-dimensional complex Hilbert space, one writes