# Most common vector spaces in functional analysis

#### ModusPonens

##### Well-known member
Hello

I'm happy to inaugurate the analysis forum

What are the most common vector spaces in functional analysis?

I also have another question: is it necessary to know measure and integration before a first course in functional analysis?

#### Ackbach

##### Indicium Physicus
Staff member
The initial motivation for developing functional analysis was quantum mechanics, and the $L^{2}$ Hilbert space as used in quantum mechanics is still extremely important in functional analysis. All Hilbert spaces are also vector spaces, but with some additional structure on top.