← GATE Mathematics guide GATE Mathematics · Section 7
Functional Analysis
Banach & Hilbert space theory and the classical theorems — directly covered.
Books that cover Section 7
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Full syllabus — Section 7
- Normed linear spaces; bounded and compact linear operators; Banach spaces; separability; dual spaces
- Hahn–Banach theorem; open mapping and closed graph theorems; principle of uniform boundedness
- Inner-product spaces; Hilbert spaces; orthonormal bases; projection theorem; Riesz representation theorem; spectral theorem for compact self-adjoint operators