Functional Analysis
by Walter Rudin · Walter Rudin
Walter Rudin's graduate text on functional analysis, covering topological vector spaces, distributions and Fourier transforms, Banach algebras, and spectral theory of operators on Hilbert space. Readers learn the abstract framework underlying modern analysis and PDE, with demanding exercises.
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More resources on Banach Spaces
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
Terry Tao's Blog on Banach Spaces
A tag archive on Terence Tao's blog, currently holding one post that uses the closed graph theorem to show a vector space admits at most one compatible Banach norm. Suited to readers who know basic functional analysis and want a short, rigorous example.
nLab: Banach Space
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