Hilbert spaces

Abbreviation: Hilb

Definition

A Hilbert space is a vector spaces $\mathbf{H}$ with inner product $\langle\cdot , \cdot\rangle$, which is complete in the corresponding metric.

Remark:

Morphisms

Let $\mathbf{H_1}$ and $\mathbf{H_2}$ be two Hilbert spaces. A morphism from $\mathbf{H_1}$ to $\mathbf{H_2}$ is a bounded operator $T:H_1\rightarrow H_2$.

Examples

Example 1:

Basic results

Feel free to add or delete properties from this list. The present list may contain properties that are not relevant to the class that is being described.

Properties

Subclasses

Superclasses

[[Banach spaces]] 

References

External links