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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
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. Jan Hamhalter
Class:	M Mgr. MA M Mgr. MA > Volitelné
Classification:	Mathematics > Functional Analysis, Topology and Category
Incompatibility :	NRFA082
Interchangeability :	NRFA082
Is interchangeable with:	NRFA082

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Annotation -

Last update: T_KMA (02.05.2013)

C*-algebras, spaces of operators, trace duality, von Neumann algebras.

Course completion requirements - Czech

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

Předmět je zakončen zkouškou.

Literature - Czech

Last update: T_KMA (02.05.2013)

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

Requirements to the exam - Czech

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

Zkouška bude ústní formou v rozsahu odpřednesené látky.

Syllabus -

Last update: T_KMA (25.04.2013)

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

Entry requirements -

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

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