MAGIC040: Operator Algebras

Course details

A specialist MAGIC course


Autumn 2011
Monday, October 10th to Friday, December 16th


Live lecture hours
Recorded lecture hours
Total advised study hours


13:05 - 13:55


I. C*-algebras (3 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, characterizing abstract C*-algebras
  5. Ideals and approximate units
  6. Multipliers
  7. Tensor products

II. Completely bounded and completely positive maps (3 lectures)
  1. Positivity/boundedness and complete positivity/boundedness
  2. The Stinespring representation theorem and Arveson extension theorem
  3. The Wittstock decomposition theorem for completely bounded maps, and the Haagerup-Paulsen-Wittstock theorem

IV. Operator Spaces and Algebras (4 lectures)
  1. Abstract vs concrete operator spaces, systems and algebras
  2. The Effros-Ruan theorem, characterizing abstract operator systems
  3. Ruan's theorem, characterizing abstract operator spaces
  4. The Blecher-Ruan-Sinclair theorem, characterizing abstract operator algebras


A working knowledge of functional analysis and operator theory, as well as some topology, as provided in, for example, MAGIC061. We lightly skirt over some of this material in the first couple of lectures.


No syllabus information is available yet.


  • MD

    Dr Michael Dritschel

    University of Newcastle


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The assessment for this course will be released on Monday 21st September 2020 and is due in by Friday 16th December 2011 at 23:59.

Throughout the lectures you will find s in the margins. These indicate material that has been stated without justification. You are asked to fill in the details on as many of these as you can. The material will be collected at the end of the semester, and you are asked to provide your work in electronic form as a pdf file, preferably produced from a TeX source file.

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