MAGIC040: Operator Algebras

Course details

A specialist MAGIC course

Semester

Spring 2009
Monday, January 19th to Friday, March 27th; Monday, April 27th to Monday, April 27th

Hours

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

Timetable

Mondays
13:05 - 13:55
Tuesdays
13:05 - 13:55

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

Follow the link for a book to take you to the relevant Google Book Search page

You may be able to preview the book there and see links to places where you can buy the book. There is also link marked 'Find this book in a library' - this sometimes works well, but not always - you will need to enter your location, but it will be saved after you do that for the first time.

Assessment

Attention needed

Assessment information will be available nearer the time.

Files

Only consortium members have access to these files.

Please log in to view course materials.

Lectures

Please log in to view lecture recordings.