M0999 A Course in Operator Theory

Faculty of Science
Spring 2024
Extent and Intensity
2/0/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
Anindya Biswas, M.Sc., Ph.D. (lecturer)
Guaranteed by
doc. Ilja Kossovskij, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. Ilja Kossovskij, Ph.D.
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 19. 2. to Sun 26. 5. Tue 18:00–19:50 M5,01013
Prerequisites
M4100 Mathematical Analysis IV && M6150 Functional Analysis I
M4100 Mathematical Analysis IV: Notion of measure and integration, the convergence theorems, the notion of L^p spaces, Riesz–Markov–Kakutani representation theorem.
M6150 Functional Analysis I: Basic properties of Banach and Hilbert spaces and bounded linear operators on those spaces, Hahn-Banch separation and extension theorems, open mapping and closed graph theorem, uniform boundedness principle.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Syllabus
  • Bounded linear operators and their spectrum, analytic functional calculus, the square root and the polar decomposition.
  • Compact operators on Hilbert spaces, Hilbert–Schmidt operators, trace class operators, singular values and the canonical decomposition.
  • The spectral theorems for self-adjoint and normal operators.
  • Gelfand transform, C*-algebras and Gelfand-Naimark-Segal construction.
Literature
  • John B. Conway, A course in operator theory, Grad. Stud. Math., 21, American Mathematical Society, Providence, RI, 2000. xvi+372 pp.
  • SIMON, Barry. Operator theory : a comprehensive course in analysis. Providence, Rhode Island: American Mathematical Society, 2015, xviii, 749. ISBN 9781470411039. info
  • CONWAY, John B. A course in functional analysis. 2-nd ed. New York: Springer - Verlag, 1990, xvi, 399. ISBN 0387972455. info
Language of instruction
English
Further Comments
The course is taught only once.
  • Enrolment Statistics (recent)
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