I am looking for a good book for junior-senior US math majors on functional analysis. Some background and detail:
Last semester I taught a special topics course in functional analysis to junior-senior level math majors. It was the first time teaching functional analysis both for me and for my institute as a whole. I used the book Linear Functional Analysis by Rynne and Youngson, partly because I like the overall structure and partly because my students can get Springer e-books for free through my institute's library, and as much as possible I try to support and facilitate free, open information.
Rynne and Youngson is a nice book, but the issue I encountered is that for most US undergraduates, it assumes more preparation than they are likely to have (I think it is really meant for UK undergraduates, who specialize sooner). For example, it assumes you already know what $L^p$ spaces are and just need a quick reminder. My students had had one semester of real analysis at most, so I ended up writing a lot of material for them on metric spaces, measure theory, Lebesgue integration, etc.
For another run of the course, I am looking for an alternate book I could use instead, that would include a more detailed treatment of background information. It would also be good for the book to be somewhat geared toward the application of functional analysis to PDE, though the students last semester loved learning about the more pure aspects of infinite-dimensional Banach spaces, so it doesn't have to be super applied.
Recommendations? I saw mention on this site of Kreysig, which looks good but I am slightly worried about availability after looking on Amazon. A nice bonus would be if the book has an e-version I can get the library to buy so that students can use it for free.
Thanks so much in advance!!