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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


Autumn 2019 (Monday, October 7 to Friday, December 13)


  • Live lecture hours: 10
  • Recorded lecture hours: 0
  • Total advised study hours: 40


  • Thu 10:05 - 10:55


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.


See description.

Other courses that you may be interested in:


Michael Dritschel
Phone (0191) 2227229
Interests operator theory, operator algebras, function theory
Photo of Michael Dritschel


C*-algebras and operator theoryMurphy
C*-algebras by exampleDavidson
Fundamentals of the Theory of Operator Algebras: Elementary theoryKadison and Ringrose
Fundamentals of the Theory of Operator Algebras: Advanced theoryKadison and Ringrose
Completely bounded maps and operator algebrasPaulsen
Hilbert C*-modules: a toolkit for operator algebraistsLance
Hilbert C*-modulesManuĭlov and Troit︠s︡kiĭ
Operator algebras and their modules: an operator space approachBlecher and Merdy
Operator algebras: theory of C*-algebras and von Neumann algebrasBlackadar
What are operator spaces?G. Wittstock, et al.


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Recorded Lectures

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