I love this one https://ia801706.us.archive.org/7/items/in.ernet.dli.2015.141134/2015.141134.Optimization-By-Vector-Space-Methods_text.pdf https://ia801706.us.

I love this one https://ia801706.us.archive.org/7/items/in.ernet.dli.2015.141134/2015.141134.Optimization-By-Vector-Space-Methods_text.pdf 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.