← GATE Mathematics guide GATE Mathematics · Section 7

Functional Analysis

Banach & Hilbert space theory and the classical theorems — directly covered.

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