MAGIC040: Operator Algebras

Course details

A specialist MAGIC course

Semester

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

Hours

Live lecture hours
10
Recorded lecture hours
0
Total advised study hours
0

Timetable

Thursdays
13:05 - 13:55

Description

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

Prerequisites

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.

Syllabus

No syllabus information is available yet.

Lecturer

  • MD

    Dr Michael Dritschel

    University
    University of Newcastle

Bibliography

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Assessment

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.

Please note that you are not registered for assessment on this course.

Files

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Lectures

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