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I've completed both the functional analysis bits of Rudin's functional analysis fold's real analysis and am looking for the next step in operator theory. My question is: what textbooks can be recommended beyond the level above mentioned? Looking for one as algebraic as possible, i.e. really looks at the structure and isn't afraid to employ machinery (e.g. category theory)

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  • $\begingroup$ If you are looking for smt as algebraic as possible any introduction to the representation theory of algebras might fit to your needs. Curtis-Reiner or Fulton-Harris might be suitable choices $\endgroup$ – KonKan Sep 16 '16 at 19:45
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There is this book https://www.amazon.com/Exercises-Functional-Translations-Mathematical-Monographs/dp/0821840983/ref=sr_1_1?s=books&ie=UTF8&qid=1473992473&sr=1-1&keywords=lectures+and+exercises+in+functional+analysis which might be what you need. However, I can't guarantee it's a level above Rudin.

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