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Course Descriptions

16:640:509 - Topics in Analysis

Eric Carlen


Operator Algebras, Theory and Application

Course Description:

This course will provide an introduction to fundamental results in the theory of operator algebras and to topics of current active research interest, both in pure mathematics and mathematical physics, especially quantum information theory. There will be no textbook, but a detailed set of notes and references to research papers will be provided. This will be available in the middle of the Fall semester, well in advance of the beginning of the course.


Dear Graduate Students,

I have created a class web-page for the section of 509 that will have the course title  "Positive Maps on Operator Algebras an Quantum Markov Semigroups"

The web page for the course is at

On this page there is a link to a detailed course description. The course will be accessible to students who have taken 502, or are taking it concurrently. No prior knowledge of operator algebras is assumed. Despite this, the course is intended as an introduction to an active field of research, intended to impart knowledge of  state-of-the-art techniques in this area of analysis, and also of the many open problems in the field, as well as some in applications to mathematical physics.

There is also a link to the notes for the course, which I am presenting in a fully fleshed-out text form, except that the exercises will be in the homework assignments. The first two chapters are posted. The link is on the course page. I will post at least two more chapters before the course begins, getting into part 2 of this 3 part course. (See the course description.) I will keep well-ahead of the lectures so that students may read ahead. There is no single text that is suitable for this course, hence the notes.

If you have any questions, do not hesitate to ask,

Best regards, Eric Carlen


None; see above




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Department of Mathematics
Rutgers University
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