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hilbert_spaces [2010/07/29 15:46] (current)
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 +=====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]