[srean]

I love this one

https://ia801706.us.archive.org/7/items/in.ernet.dli.2015.14...

Luenberger, Optimization By Vector Space Methods.

Although it is about a specific application, optimization, it is a good book to get a sense of infinite dimensional vector spaces. I would also recommend Halmos. His book surreptitiously introduces you to that subset of linear algebraic notions that survive inti infinite dimensional spaces.