Which Branch of Math Should I Study for a Foundation in Functional Analysis?

[houlahound]

looking at notes on functional analysis for self study. the authors I have stumbled across so far launch straight into the formal theory. I can't find any middle ground of intuitive motivations for the theory as yet. I am assuming the following is part of set theory? I can't follow the arguments because I don't know the terminology. are there lists defined for example the symbols in the following. I do not want these particular ones defined I want to know how to do it myself.

what branch of math do I need to read to get a foundation in this language.

any recommended readings.

thanks any leads.

 

[Mark44]

The \ symbol is "set difference" so A \ B = A ∩ B^C (the elements of A intersected with the complement of B)

∩_α F_α means $F_{\alpha_1} \cap F_{\alpha_2} \cap \dots F_{\alpha_n} \cap \dots$, where the $\alpha_i$s are some indexing set.
∪_α F_α is similar, but is the union over some indexing set.

Books on analysis usually define these symbols in an appendix.

 

[micromass]

∩_α F_α means $F_{\alpha_1} \cap F_{\alpha_2} \cap \dots F_{\alpha_n} \cap \dots$, where the $\alpha_i$s are some indexing set.

Correct, but this gives the impression that the number of $F_\alpha$ is countable, while it can be much more general. In any case, it seems the OP will need to look at some basic set theory before he can handle analysis.

 

[Mark44]

Correct, but this gives the impression that the number of $F_\alpha$ is countable, while it can be much more general.

Yes, I realize that the $\alpha$'s are some indexing set, not necessarily a countable set. My intent was to expand the notation somewhat.

 

[houlahound]

Does analysis solve problems or just prove theorems and provide tools for solving problems?

ETA, I am going to do classical analysis on real numbers first re calculus. Seems like the logical thing and apparently I am already familiar with many of the content eg limits, series, real numbers etc.

Then set theory/logic then analysis.

Sound sound?