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Can you recommend a gentle introduction to the abstract thinking and motivation of functional analysis? I'm looking for a book that holds you by the hand and shows the details of exercises, etc.


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up vote 5 down vote accepted

Of the well written books on Functional analysis that I've seen, Kreyszig is the most elementary. The Amazon reviews seem to agree with me.

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Erwin Kreyszig Introductory Functional Analysis or Rynne & Youngson Linear Functional Analysis.

Both are elementary, well-written and self-contained.

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I would recommend Introduction to Functional Analysis by S.C. Bose. The text is really good and simple to understand; there is a considerable number of solved exercises and examples. I'm getting a desire to re-read!

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