Functional analysis 2
Code  Completion  Credits  Range  Language 

01FAN2  Z,ZK  5  2P+2C  Czech 
 Vztahy:
 In order to register for the course 01FAN2, the student must have successfully completed or received credit for and not exhausted all examination dates for the course 01FANA1. The course 01FAN2 can be graded only after the course 01FANA1 has been successfully completed.
 In order to register for the course 01FAN3, the student must have successfully completed or received credit for and not exhausted all examination dates for the course 01FAN2.
 Garant předmětu:
 Lecturer:
 Tutor:
 Supervisor:
 Department of Mathematics
 Synopsis:

The course aims to present selected fundamental results from functional analysis including basic theorems of the
theory of Banach spaces, closed operators and their spectrum, HilbertSchmidt operators, spectral decomposition
of bounded selfadjoint operators.
 Requirements:
 Syllabus of lectures:

1. The Baire theorem, the BanachSteinhaus theorem (the principle of uniform boundedness), the open mapping
theorem, the closed graph theorem.
2. Spectrum of closed operators in Banach spaces, the graph of an operator, analytic properties of a resolvent,
the spectral radius.
3. Compact operators, the ArzelaAscoli theorem, HilbertSchmidt operators.
4. The Weyl criterion for normal operators, properties of spectra of bounded selfadjoint operators.
5, The spectral decomposition of bounded selfadjoint operators, functional calculus.
 Syllabus of tutorials:
 Study Objective:
 Study materials:

Povinná literatura
1. J. Blank, P. Exner, M. Havlíček: Hilbert Space Operators in Quantum Physics, Springer, 2013.
2. B. Simon: Operator Theory: A Comprehensive Course in Analysis, Part 4, AMS, Rhode Island, 2015.
Doporučená literatura
3. W. Rudin: Real and Complex Analysis, (McGrewHill, Inc., New York, 1974)
4. A. N. Kolmogorov, S. V. Fomin: Elements of the Theory of Functions and Functional Analysis, (Dover
Publications, 1999)
5. A. E. Taylor: Introduction to Functional Analysis, (John Wiley and Sons, Inc., New York, 1976)
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Aplikovaná algebra a analýza (compulsory course in the program)
 Matematické inženýrství  Matematická fyzika (PS)
 Matematické inženýrství  Matematická informatika (elective course)
 Matematické inženýrství  Matematické modelování (PS)