Introduction to Mathematical Physics/Vectorial spaces

Definition

Let $K$ be $R$ of $C$. An ensemble $E$ is a vectorial space if it has an algebric structure defined by to laws $+$ and $.$, such that every linear combination of two elements of $E$ is inside $E$. More precisely:

Functional space

Template:IMP/defn The set of the function continuous on an interval is a functional space. The set of the positive functions is not a fucntional space. Template:IMP/defn $<T|\varphi >$ designs the number associated to function $\varphi$ by functional $T$. Template:IMP/defn