Course Identification

Topics in Operator Algebras
20224211

Lecturers and Teaching Assistants

Dr. Guy Salomon, Prof. Uri Bader
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Course Schedule and Location

2022
First Semester
Sunday, 14:00 - 16:30, Goldsmith, Rm 208
24/10/2021
18/03/2022

Field of Study, Course Type and Credit Points

Mathematics and Computer Science: Lecture; Elective; Regular; 3.00 points

Comments

N/A

Prerequisites

Basic courses in functional analysis and measure theory

Restrictions

25

Language of Instruction

English

Attendance and participation

Expected and Recommended

Grade Type

Pass / Fail

Grade Breakdown (in %)

50%
50%
Assignments + Presentation (depending on the number of participants)

Evaluation Type

Other

Scheduled date 1

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-
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Estimated Weekly Independent Workload (in hours)

4

Syllabus

What is this course all about?

An operator algebra on a Hilbert space H is a closed subalgebra of the algebra B(H) of bounded operators on H. These include all closed algebras of continuous functions on a compact space, matrix algebras, and many more. My intention is to divide the course into two halves: the first will focus on operator algebras, with the first few weeks dedicated to self-adjoint ones, namely C*-algebras, and the second will be devoted to the fruitful interaction between operator algebras and groups

The very flexible plan is:

  • C*-algebras (3–5 lectures)
  • Operator algebras and operator systems (3–4 lectures)
  • Groups, dynamics, and related operator algebras (5–7 lectures) 

Learning Outcomes

Upon successful completion of this course students should be able to
demonstrate an understanding of the concepts of operator algebras as well as their relations to dynamics.

Reading List

  1. D. P. Blecher and C. L. Merdy. Operator Algebras and Their Modules — An Operator Space Approach. The Clarendon Press, Oxford University Press, Oxford, 2004.
  2. E. Breuillard, M. Kalantar, M. Kennedy, and N. Ozawa. C*-simplicity and the unique trace property for discrete groups. Publ. Math. Inst. Hautes Études Sci., 126:35–71, 2017.
  3. N. P. Brown and N. Ozawa. C*-algebras and Finite-Dimensional Approximations. American Mathematical Society, Providence, 2008.
  4. K. R. Davidson. C*-algebras by example, volume 6 of Fields Institute Monographs. American Mathematical Society, Providence, RI, 1996.
  5. M. Kalantar and M. Kennedy. Boundaries of reduced C ∗ -algebras of discrete groups. J. Reine Angew. Math., 727:247–267, 2017.
  6. V. Paulsen. Completely Bounded Maps and Operator Algebras, volume 78 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 2002.

Website

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