Abbreviation: Hilb

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

Remark:

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 $T:H_1\rightarrow H_2$.

Example 1:

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.

[[Banach spaces]] 

[http://mathworld.wolfram.com/HilbertSpace.html MathWorld Hilbert Spaces]

[http://www.wikipedia.org/wiki/Hilbert_space Wikipedia Hilbert Spaces]