MAGIC040: Operator Algebras

Course details

Semester

Spring 2014
Monday, January 20th to Friday, March 28th

Hours

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

Timetable

Tuesdays
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

Description

The assessment for this course will be via a single take-home paper in April with 2 weeks to complete and submit online. There will be 7 questions and you will need to the equivalent of 4 questions to pass.

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Files

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Lectures

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