# Differences

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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]

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