### Course announcement: Operator Spaces, Operator Algebras and Related Topics (Topics in Operator Theory 106435)

#### by Orr Shalit

Next week I will begin teaching a topics course “Topics in Operator Theory – 106435”. This is an advanced graduate course, where “advanced” means that I expect students to be familiar with graduate functional analysis.

The official name of the course is “Topics in Operator Theory” but the true title is “Operator Spaces, Operator Algebras and Related Topics”. There are two somewhat competing goals driving this course: the first goal is to give students a taste of the beautiful subjects of operator spaces and operator algebras, broadening their view of functional analysis, and giving those who wish enough tools to delve into the literature in this subject. The second goal is to train students to understand the problems in which I am interested and to get acquainted with the methods of the theory so that they will be able to carry out research in my group. The choice of topics will therefore be somewhat eclectic. In fact, I have several different plans for this course, and I am keeping things vague on purpose so that I am free to change course as the wind blows (and as I see who the students are, what their background is and where their interests lie).

What else? The course will be given in English. There is no official web page for the course – I might open exercises online on this blog. The grade will be based on some exercises that I will give throughout the semester, and a final “big homework” project.

dear mr shalit,

will you be posting your lecture notes here on this blog? It would be great to personally work through your notes online since i can’t visit your course.

Thanks for this amazing blog by the way. I really enjoy reading your posts and the way you think about mathematics.

greeting,

moe

Thanks moe. I hope to post, let’s see how much time I find for this.

[…] von Neumann’s inequality holds for every contraction, then $latex E must be a Hilbert space (a result of Foias ). So if is not a Hilbert space, there exists such that is not an operator […]

Dear Orr,

Now that the course “Topics in Operator Theory” is over, I hope that it was good for you and the students. In this connection, and since you like very much operator theory, and also because the name of your blog is “Noncommutative Analysis”, it might be of some value to ask you the following question: are you aware of the book called “Non-commutative Analysis”, by Palle Jorgensen and Feng Tian, World Scientific Publishing Company, 2017?

According to some reviews, this book seems rather interesting and relevant to you, and possibly to other people working in this field (or ones who consider working in this field).

Here are some links in which the book can be found, in either electronic form, or paperback, or used form, etc. (and probably there are additional places from which one can get this book):

https://www.barnesandnoble.com/w/non-commutative-analysis-palle-jorgensen/1124788056

In the second link above there is a review of one of the costumers, and another review can be found in the link below (page 409):

http://www.cs.ubbcluj.ro/~studia-m/index.php/journal/article/download/294/pdf

Best regards and good luck!

Dear Daniel,

Thanks for bring this book to my attention, I was not aware of it. I will check it out.

Best,

Orr