Functional Analysis: An Introduction
by Yuli Eidelman, Vitali Milman, Antonis Tsolomitis · Yuli Eidelman, Vitali Milman, Antonis Tsolomitis
An AMS graduate textbook introducing functional analysis through Banach and Hilbert spaces, the Hahn–Banach, open mapping and uniform boundedness theorems, compact operators, and spectral theory. It suits students finishing real analysis who want a structured first course with exercises.
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More resources on Banach Spaces
Wolfram MathWorld
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Terry Tao's Blog on Banach Spaces
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