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Functional Analysis I - MAT4841

Honours Year module NQF level: 8 Credits: 12
Module presented in English Module presented online
Purpose: To enable learners to master and apply the fundamental concepts of linear and metric spaces. The metric (or topological) structure of a space involves the concepts of continuity, convergence, compactness and completeness. The structure of Banach spaces, linear operators defined on Banach spaces and linear functions defined on Banach spaces with range contained in the set of complex numbers are studied. The latter functions are called functionals. We also concentrate on a specific Banach space, the Hilbert space, where orthogonality, ortonormality, separability and classes of bounded linear operators (defined by using the Hilbert-adjoint operator) are studied.