Rudin skips steps. Every time you see "It is obvious that...", stop and prove it to yourself. His three-word justifications often hide half a page of dense logic.
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Have you worked through Rudin’s Functional Analysis? What was your experience? Comment below. Rudin skips steps
A significant portion of the work is dedicated to the behavior and properties of transformations between these abstract spaces. Here’s a solid, informative post suitable for a
The book is divided into three primary sections that progress from foundational theory to specialized applications: Internet Archive Part I: General Theory
Perhaps one of the most daunting topics in analysis, the theory of unbounded operators is handled with Rudin’s characteristic clarity (though "clarity" here implies rigorous logic rather than easy reading). This chapter is indispensable for anyone studying mathematical physics.