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Lecturer(s)
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Ludvík Pavel, RNDr. Ph.D.
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Vodák Rostislav, RNDr. Ph.D.
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Course content
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1. Metric spaces, complete metric spaces, compactness, continuous operators, Banach Fixed Point Theorem. 2. Linear spaces, basis, direct sum, linear operators and functionals, extension of linear functionals, projections, alpha and delta index of a linear operator. 3. Normed linear spaces, Banach spaces, complete hull, continuous linear operators, inverse operators. 4. The space of continuous linear operators, dual spaces, the Hahn-Banach Theorem and its consequences. 5. Canonical mappings, reflexive spaces. 6. Weak convergence. 7. Spaces with scalar products, Hilbert spaces, orthogonal systems, Fourier series, orthogonal projections, the Riesz Representation Theorem. 8. Adjoint operators. 9. Completely continuous linear mappings.
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Learning activities and teaching methods
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Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming)
- Attendace
- 52 hours per semester
- Preparation for the Course Credit
- 30 hours per semester
- Homework for Teaching
- 30 hours per semester
- Preparation for the Exam
- 70 hours per semester
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Learning outcomes
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Master basic methods and tools of linear functional analysis.
Comprehension Understand the mathematical theory of linear operators in linear spaces.
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Prerequisites
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Understanding the basic elements of mathematical analysis including the mathematical tools of differential and integral calculus.
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Assessment methods and criteria
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Oral exam, Written exam
Credit: active participation, homework. Exam: written test, the student has to understand the subject and be able to prove principal results.
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Recommended literature
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A. Sasane. (2017). Friendly Approach To Functional Analysis. WSPC.
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B. D. Reddy. (1998). Introductory Functional Analysis: With Applications to Boundary Value Problems and Finite Elements. Springer.
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E. Kreyszig. (1989). Introductory Functional Analysis with Applications. Wiley.
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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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