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Course, academic year 2023/2024
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Operator Algebras 1 - NMMA561
Title: Operátorové algebry 1
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023 to 2023
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: prof. RNDr. Ondřej Kalenda, Ph.D., DSc.
prof. RNDr. Jiří Spurný, Ph.D., DSc.
prof. RNDr. Jan Hamhalter, CSc.
Class: M Mgr. MA
M Mgr. MA > Volitelné
Classification: Mathematics > Functional Analysis, Topology and Category
Incompatibility : NRFA082
Interchangeability : NRFA082
Is interchangeable with: NRFA082
Annotation -
C*-algebras, spaces of operators, trace duality, von Neumann algebras.
Last update: T_KMA (02.05.2013)
Course completion requirements - Czech

Předmět je zakončen zkouškou.

Last update: Spurný Jiří, prof. RNDr., Ph.D., DSc. (06.10.2017)
Literature - Czech

Fillmore, P. A.: A user's guide to operator algebras, John Wiley & Sons, Inc., New York, 1996

Kadison, R. V., Ringrose, J. R.: Fundamentals of the theory of operator algebras. Vol. I. Elementary theory. Reprint of the 1983 original, American Mathematical Society, Providence, RI, 1997

Kadison, R. V., Ringrose, J. R.: Fundamentals of the theory of operator algebras. Vol. II. Advanced theory. Corrected

reprint of the 1986 original, American Mathematical Society, Providence, RI, 1997

Meise R., Vogt D. : Introduction to functional analysis, Oxford University Press, New York, 1997

Last update: T_KMA (02.05.2013)
Requirements to the exam - Czech

Zkouška bude ústní formou v rozsahu odpřednesené látky.

Last update: Spurný Jiří, prof. RNDr., Ph.D., DSc. (06.10.2017)
Syllabus -

C* algebras - definition, properties, automatic continuity, positive elements, approximate unit, basic properties of spaces of operators, operator topologies, duality, von Neumann algebras, von Neumann bicommutant theorem, Kaplansky density theorem

Last update: T_KMA (25.04.2013)
Entry requirements -

A sound knowledge of functional analysis (Banach and Hilbert spaces, bounded linear operators) and general topology (including compactness).

Last update: Kalenda Ondřej, prof. RNDr., Ph.D., DSc. (23.05.2019)
 
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