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Lecturer(s)
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Staněk Svatoslav, prof. RNDr. CSc.
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Vodák Rostislav, RNDr. Ph.D.
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Course content
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1. The Closed graph theorem. 2. The uniform boundedness principle. 3. Reflexive spaces. 4. The Eberlein-Šmulian 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.
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Learning activities and teaching methods
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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
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Learning outcomes
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Understand the principles of functionaal analysis and fixed point theorems.
Comprehension Understand the principles of functional analysis, spectral theory and fixed point theorems.
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Prerequisites
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Basic notions of functional analysis.
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Assessment methods and criteria
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Oral exam, Dialog
Credit: active participation, homework solving. Exam: the student has to understand the subject and be able to prove the principal results.
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Recommended literature
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E. Zeidler. (1999). Applied Functional Analysis, Applications to Mathematical Physics. Springer.
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E. Zeidler. (1995). Applied Functional Analysis, Main Principles and Their Applications. Springer.
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J. Lukeš. (2001). Zápisky z funkcionální analýzy. MatFyzPress.
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P. Drábek, J. Milota. (2004). Lectures on Nonlinear Analysis. Plzeň.
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