functional analysis | Asaf Karagila

Posts tagged functional analysis

Zornian Functional Analysis coming to arXiv!

Oct 07 2020, 15:23

Back in autumn 2015 I took a functional analysis course with Prof. Matania Ben-Artzi, and he let me write a term paper about uses of the axiom of choice in functional analysis for my final grade. One year later, in October 2016, I finally posted the note here. It then received some feedback from some people, and about a year after that I posted a small revision.

Earlier this week I suggested my note as a source for the proof that the Baire Category Theorem is equivalent to Dependent Choice. After doing that, I stumbled upon an errata by Theo Bühler and Dietmar A. Salamon to their Functional Analysis book, which refers to my write-up.

New notes online!

Jul 22 2019, 17:40

I have posted two new lecture notes online. The one is from a course in functional analysis I took in the autumn of 2015/16 with Prof. Matania Ben-Artzi, and the second is from the course I taught in axiomatic set theory in the autumn of 2016/17.

Just as a general caveat for the set theory notes, since all the students in the course were also my students in the basic set theory course that I taught with Azriel Levy (yes, that Azriel Levy, and yes it was quite an awesome experience) and there I managed to cover some fairly nontrivial things in that course, these notes might feel as if there are some gaps there, or that I skip here and there over some information.

Zornian Functional Analysis or: How I Learned to Stop Worrying and Love the Axiom of Choice

Oct 10 2016, 19:34

Back in the fall semester of 2015-2016 I had taken a course in functional analysis. One of the reasons I wanted to take that course (other than needing the credits to finish my Ph.D.) is that I was always curious about the functional analytic results related to the axiom of choice, and my functional analysis wasn't strong enough to sift through these papers.

I was very happy when the professor, Matania Ben-Artzi, allowed me to write a final paper about the usage of the axiom of choice in the course, instead of taking an exam.