Mathematics: Linear Functional Analysis

Education facts

Code: MATP35

<p>The course presents the principles of functional analysis and their applications. These include the basic properties of Banach and Hilbert spaces as well as the spectral theory of bounded and compact linear operators.  </p><p>The course treats fundamental properties of Banach and Hilbert spaces and the bounded linear operators defined on them:</p> <ul> <li>Banach spaces, the Hahn-Banach Theorem, weak convergence and  weak precompactness of the unit ball.</li> <li>Hilbert spaces. Examples including L2 spaces. Orthogonality, orthogonal complement, closed subspaces, projection theorem. Riesz Representation Theorem.</li> <li>Orthonormal sets, Bessel's inequality. Complete orthonormal sets, Parseval's identity.</li> <li>Baire Category Theorem and its consequences for operators on Banach spaces (uniform boundedness, open mapping, inverse mapping and closed graph theorems). Strong convergence of sequences of operators.</li> <li>Bounded and compact linear operators on Banach spaces and their spectra.</li> <li>The spectral theorem for compact self-adjoint operators on Hilbert spaces.</li> </ul>

Entry requirements

At least 90 credits in pure mathematics including knowledge corresponding to a course in Integration Theory, 7.5 credits (Lebesgue integral). English 6/English course B.

Education offerings

Each offering has its own dates and conditions. Closed offerings are retained as history and do not mean that a new application is open.

• Mathematics: Linear Functional Analysis

  Lund University

  Start date: 31 August 2026

  End date: 17 January 2027

  Pace of study: 25 %