Noncommutative Analysis

Month: September, 2012

Worse than Elsevier

Recently, I received the following email:

Dear Dr. Shalit,

I am writing to inquire whether you have received our previous email inviting you to submit an article to the Special Issue on “Uncertain Dynamical Systems: Analysis and Applications,” which will be published in Abstract and Applied Analysis, and the deadline for submission is October 19th, 2012.

Looking forward to hearing from you.

Best regards,

************

To this, I replied:

Dear ************,
I am sorry, I did not realized that you were waiting for an answer from me.
The special issue sounds interesting, but I do not submit papers to journals that require processing charges from the authors.
Best regards,
Orr Shalit

This has been my opinion for a long time, and it didn’t change when Gowers and Tao joined the bad guys. Here’s what I think is bad about the publishing model where authors pay to have their papers published.

  1. There is an obvious conflict of interests here, which might corrupt science.
  2. These journals always seemed to me to be a nasty way to wring money out of mathematicians that either don’t know better, don’t believe in their own worth, or couldn’t (for some reason) publish their work in a normal journal.
  3. It will decrease mobility: it creates another obstacle for mathematicians with no grant money or from weaker institutions, making it harder for them to eventually get grants and move to perhaps stronger institutions.
  4. And even if I do have grant money, that’s not how I want to spend it.

And don’t tell me that in the eighteenth century or ancient Greece scientists payed to have their work published: because here people are not paying to have their work published – everybody’s work is published on the web if they wish it – here people are paying to have their work published inside a journal, meaning that they are buying their work’s credibility.

Only two good things about this model. First, it is open-access, which is great, but as I’ve said that doesn’t matter any more, since all papers are open access anyway (even if the official journal version isn’t). Second good thing, and this is really a good thing: in this model people have to think about what they are sending for publication, because publishing also has a price. So hopefully this can create eventually a situation where people publish a little less papers, but these papers are more complete and contain less repetition.

That last point is really is something to think about. I can think of at least one different means of attaining this goal: tenure.

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Functional Analysis – Introduction. Part I

I begin by making clear a certain point. Functional analysis is an enormous branch of mathematics, so big that it does not seem appropriate to call it “a branch”, it sometimes looks more like another tree. When I will talk below about functional analysis, I will mean “textbook functional analysis” and not “research functional analysis”. By this I mean that I will only refer to the core of the theory which is several decades old and which is more-or-less agreed to be the essential and basic part of the subject.

The goal of this post is to serve as an introduction to the course “Advanced Analysis, 201.2.5401”, which is a basic graduate course on (textbook) functional analysis. In the lectures I will only have time to give a limited description of the roots of the subject and the motivation will have to be brief. Here I will aim to describe what was the climate in which this tree grew, where are its roots and what are its fruits.

To prepare this introduction I am relying on the following sources. First and foremost, my love of the subject and my point of view on it were strongly shaped by my teachers, and in particular by Boris Paneah (my Master’s thesis advisor) and Baruch Solel (my PhD. thesis advisor). Second, I learned a lot on the subject from the book “Mathematical Thought from Ancient to Modern Times” by M. Kline and from the notes sections of Rudin’s and Reed-Simon’s books “Functional Analysis”.

And a warning to the kids: this is a blog, not a book, and if you really want to learn something go read the books (the books I mentioned have precise references).

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Functional analysis – a preface to the introduction

I am planning to write a post that will be an introduction to the course “Advanced Analysis”, which I shall be teaching in the fall term. The introduction is to comprise two main themes: motivation and history. I was a little surprised to find out – as I was preparing the introduction – that, looking from the eyes of a student, the history of subject provided little motivation. I also began to oscillate between two opposite (and equally silly) viewpoints. The first viewpoint is that functional analysis is a big and respectable field of mathematics, which needs no introduction; let us start with the subject matter immediately since there is so much to learn. The second viewpoint is that there is absolutely no point in studying (or teaching) a mathematical theory without understanding its context and roots, or without knowing how it applies to problems outside of the theory’s borders. Pondering these, I found that I had some things to say before the introduction, which may justify the introduction or give it the place I intend.

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Course announcement : Advanced Analysis, 20125401

In the first term of the 2012/2013, I will be giving the course “Advanced Analysis” here at BGU. This is the department’s core functional analysis course for graduate students, though ambitious undergraduate students are also encouraged to take this course, and some of them indeed do. The price to pay is that we do not assume that the students know any functional analysis, and the only formal requisites are a course  in complex variables and a course in (point set) topology, as well as a course in measure theory which can be taken concurrently. The price to pay for having no requisites in functional analysis, while still aiming at graduate level course, is that the course is huge: we have five hours of lectures a week. In practice we will actually have six hours of lectures a week, because I will go abroad in the middle of the semester to this conference and workshop in Bangalore. The official syllabus of the course is as follows:

Banach spaces and Hilbert spaces. Basic properties of Hilbert spaces. Topological vector spaces. Banach-Steinhaus theorem; open mapping theorem and closed graph theorem. Hahn-Banach theorem. Duality. Measures on locally compact spaces; the dual of C(X). Weak and weak-* topologies; Banach-Alaoglu theorem. Convexity and the Krein-Milman theorem. The Stone-Weierstrass theorem. Banach algebras. Spectrum of a Banach algebra element. Gelfand theory of commutative Banach algebras. The spectral theorem for normal operators (in the continuous functional calculus form).

I plan to cover all these topics (with all that is implicitly implied), but I will probably give the whole course a little bend towards my own area of expertise, especially in the exercises and examples. We do have to wait and see who the students are and what their background is before deciding precisely how to proceed. Some notes for the course will appear (in the English language) on this blog. The official course webpage (which is in Hebrew) is behind this link.