Objectives and competences
Deepening the knowledge of fundamental concepts and results of functional analysis.
Content (Syllabus outline)
Banach spaces: vector spaces and normed spaces, completness, examples; subspaces and quotient spaces; finite dimensional normed spaces, compact sets; Banach algebras, spectrum.
Linear operators and functionals: bounded and unbounded linear operators; compact operators; uniform boundedness principle, open mapping theorem, closed graph theorem; dual, Hahn-Banach theorem, reflexive spaces.
Hilbert spaces: basic concepts and examples; orthogonality, Riesz theorem; orthonormal bases, adjoint operators.
Learning and teaching methods
? Lectures
? Tutorial
Intended learning outcomes - knowledge and understanding
Knowledge and Understanding:
? Banach spaces
? Hilbert spaces
? Operator theory
Intended learning outcomes - transferable/key skills and other attributes
Transferable/Key Skills and other attributes:
The obtained knowledge is a basis for both theoretical and applied analysis on an advanced level.
Readings
B. Brown, A. Page, Elements of functional analysis, Van Nostrand, 1970.
M. Hladnik, Naloge in primeri iz funkcionalne analize in teorije mere, DMFA, 1985.
B. P. Rynne, M. A. Youngson, Linear functional analysis, Springer, 2000.
J. Vrabec, Metrični prostori, DMFA, 1993.
Prerequisits
Knowledge of linear algebra and analysis.
Additional information on implementation and assessment Type (examination, oral, coursework, project):
Written exam
