# Differences

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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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