Lecturer(s)


Staněk Svatoslav, prof. RNDr. CSc.

Pastor Karel, doc. Mgr. Ph.D.

Course content

1. The Closed graph theorem. 2. The uniform boundedness principle. 3. Reflexive spaces. 4. The EberleinŠmulian theorem. 5. The Brouwer fixed point theorem. 6. Completely continuous operators. 7. The Schauder fixed point theorem and its consequences. 8. The Brouwer degree of operators. 9. Fixed point theorems in partially ordered spaces. 10. Differential calculus in normed linear spaces (Gâteaux and Fréchet derivative of operators). 11. The Implicit function theorem. 12. Spectral theory of linear and linear continuous operators in normed linear spaces and product spaces. 13. Spectral theory of linear completely continuous operators and symmetric linear completely continuous operators in normed linear spaces and product spaces.

Learning activities and teaching methods

Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming)
 Attendace
 39 hours per semester
 Preparation for the Course Credit
 10 hours per semester
 Preparation for the Exam
 40 hours per semester

Learning outcomes

Understand the principles of functionaal analysis and fixed point theorems.
Comprehension Understand the principles of functional analysis, spectral theory and fixed point theorems.

Prerequisites

Basic notions of functional analysis.

Assessment methods and criteria

Oral exam, Dialog
Credit: active participation, homework solving. Exam: the student has to understand the subject and be able to prove the principal results.

Recommended literature


J. Lukeš. (2001). Zápisky z funkcionální analýzy. MatFyzPress.

K. Deimling. (1985). Nonlinear functional analysis. Springer.

K. Najzar. (1988). Funkcionální analýza. SPN, Praha.

M. Fabian a kol. (2001). Functional Analysis and InfiniteDimensional Geometry. Springer New York.

P. Drábek, J. Milota. (2004). Lectures on Nonlinear Analysis. Plzeň.

Taylor, A. E. (1977). Úvod do funkcionální analýzy. Academia, Praha.
