MAGIC040: Operator Algebras

Course details

Semester

Spring 2010
Monday, January 11th to Friday, March 19th

Hours

Live lecture hours
20
Recorded lecture hours
0
Total advised study hours
0

Timetable

Tuesdays
13:05 - 13:55
Thursdays
13:05 - 13:55

Announcements

I've added a copy of my lecture notes from a course I give in Newcastle on topology and functional analysis. This covers in great detail the background material leading up to the Gel'fand representation theorem which I discussed in the first lecture.

Description

I. C* Algebras (6 lectures)
  1. Definitions
  2. Abstract vs concrete algebras
  3. Linear functionals, states and representations
  4. The GNS construction and the Gel'fand and Gel'fand-Naimark theorems
  5. Ideals and approximate units
  6. Multipliers
  7. Tensor products
  8. Basics of C* modules

II. Completely bounded and completely positive maps (5 lectures)
  1. Positivity/boundedness and complete positivity/boundedness
  2. Positive/CP kernels
  3. The Kolmogorov decomposition
  4. The KSGNS construction and the Stinespring representation theorem
  5. The Arveson extension theorem
  6. Voiculescu's generalisation of the Weyl-von Neumann-Berg theorem

III. Function Algebras (5 lectures)
  1. The basics of uniform algebras
  2. Extremal theory
  3. Spectral sets, distinguished varieties and dilations
  4. Reproducing kernel Hilbert spaces and multiplier spaces
  5. Realizations and interpolation

IV. Operator Spaces and Algebras (4 lectures)
  1. Abstract vs concrete spaces and algebras
  2. Families of representations
  3. Injective envelopes and boundary representations
  4. Ruan's theorem, the Blecher-Ruan-Sinclair theorem

Prerequisites

No prerequisites information is available yet.

Syllabus

No syllabus information is available yet.

Lecturer

  • MD

    Dr Michael Dritschel

    University
    University of Newcastle

Bibliography

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Assessment

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Files

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Lectures

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