Lecturer(s)


Staněk Svatoslav, prof. RNDr. CSc.

Vodák Rostislav, RNDr. Ph.D.

Course content

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 HahnBanach 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.

Learning activities and teaching methods

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

Learning outcomes

Master basic methods and tools of linear functional analysis.
Comprehension Understand the mathematical theory of linear operators in linear spaces.

Prerequisites

Understanding the basic elements of mathematical analysis including the mathematical tools of differential and integral calculus.

Assessment methods and criteria

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.

Recommended literature


A. N. Kolmogorov, S. V. Fomin. (1975). Základy teorie funkcí a funkcionální analýzy. SNTL, Praha.

Conway, J. B. (1990). A course in functional analysis. Springer.

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

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

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