I would like a functional analysis book like Terence Tao's Real Analysis and Measure Theory book, full of intuition. I am comfortable with concepts in linear algebra, real analysis, measure theory, and probability theory.
2026-03-29 22:27:52.1774823272
Intuitive functional analysis book
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For intuition, I recommend Principles of Functional Analysis by Martin Schechter. If you are interested in PDEs, there is no book better than Functional Analysis, Sobolev Spaces and Partial Differential Equations by Haim Brezis.
You might also be interested in the Methods of Modern Mathematical Physics Series by Michael Reed and Barry Simon, in particular, the first volume on Functional Analysis.
As a contrast to these, read either Conway or Rudin for clarity and economy of expression.