Course details
Semester
- Autumn 2022
- Monday, October 3rd to Friday, December 9th
Hours
- Live lecture hours
- 10
- Recorded lecture hours
- 0
- Total advised study hours
- 40
Timetable
- Thursdays
- 10:05 - 10:55 (UK)
Description
- Definitions
- Abstract vs concrete algebras
- Linear functionals, states and representations
- The GNS construction and the Gel'fand and Gel'fand-Naimark theorems, characterizing abstract C*-algebras
- Ideals and approximate units
- Multipliers
- Tensor products
- Positivity/boundedness and complete positivity/boundedness
- The Stinespring representation theorem and Arveson extension theorem
- The Wittstock decomposition theorem for completely bounded maps, and the Haagerup-Paulsen-Wittstock theorem
- Abstract vs concrete operator spaces, systems and algebras
- The Effros-Ruan theorem, characterizing abstract operator systems
- Ruan's theorem, characterizing abstract operator spaces
- The Blecher-Ruan-Sinclair theorem, characterizing abstract operator algebras
Prerequisites
We lightly skirt over some of this material in the first couple of lectures.
Syllabus
Lecturer
-
MD
Dr Michael Dritschel
- University
- University of Newcastle
Bibliography
No bibliography has been specified for this course.
Assessment
The assessment for this course will be released on Monday 9th January 2023 at 00:00 and is due in before Sunday 22nd January 2023 at 23:59.
Assessment for all MAGIC courses is via take-home exam which will be made available at the release date (the start of the exam period).
You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period).
If you have kept up-to-date with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.
Please note that you are not registered for assessment on this course.
Files
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Lectures
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