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Most common vector spaces in functional analysis


Well-known member
Jun 26, 2012

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?



Indicium Physicus
Staff member
Jan 26, 2012
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.