=====Hilbert spaces=====

Abbreviation: **Hilb**
====Definition====
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: 
  
==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====
^[[Classtype]]  |   |
^[[Amalgamation property]]  |   |
^[[Strong amalgamation property]]  |   |
^[[Epimorphisms are surjective]]  |   |

====Subclasses====
====Superclasses====
  [[Banach spaces]] 


====References====

[(Ln19xx>
)]=== External links ===
[http://mathworld.wolfram.com/HilbertSpace.html MathWorld Hilbert Spaces]

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