Talk:Tsirelson space

Comments

1. Thank you for your interest in `my space'.

2. I bother that your definition of T leaves the reader in doubt about existence and uniqueness of T, since nothing is stated about existence and uniqueness of V. In fact, such V as you define exists (which is not evident!) but is not unique.

3. About your references. Among more than 100 relevant papers you selected three (Tsirelson 1974; Figiel, Johnson 1974; Spinka 2002). I wonder, what is your selection criterion? Is the polynomial reflexivity of S(T) more important or relevant than such works as

   1989 Casazza, Shura "Tsirelson's space"
   1994 Gowers "A solution to Banach's hyperplane problem"
   1994 Odell, Schlumprecht "The distortion problem"
   1995 Odell, Schlumprecht "Distortion and stabilized structure..."
   1996 Gowers "A new dichotomy for Banach spaces"
   2001 Ortiz "An omitting types theorem for positive bounded formulas..."

and others?

4. More than 100 such references are collected on the relevant page of my site, here: [1] Maybe, an external link to it could be appropriate.

--Boris Tsirelson

Its an honour to have you comment. Articles in Wikipedia may often be incomplete or stilted; knowledgable readers are invited to make corrections and additions. In time, it is hoped that a number of editors can fashion an article that is more complete, accurate and comprehensive than any one person can easily achieve. linas 05:24, 15 Apr 2005 (UTC)

I went and did a little editing: There was a mysterious, undefined m in the definition. I replaced it with $c_{0}$ after a cursory look at Tsirelson's paper. There, he apparently uses m for an arbitrary sequence space, but quickly specialises to $m=c_{0}$ . As can be seen from Tsirelson's comments above, the page could need some more work, but I don't feel qualified. (But I went back and added a word about the existence and nonuniqueness of V.)

--Hanche 00:02, 27 January 2007 (UTC)[reply]

Maybe also look here: Gowers: A metamathematical question in Banach space theory Boris Tsirelson 09:31, 12 March 2007 (UTC)[reply]

Oy. Whatever anonymous person who edited the entry on 31 May, 2007, what a good catch! Tsirelson space is certainly not uniformly convex, as the article has said since its very beginning. On the contrary, Tsirelson's original paper clearly shows that the space has no infinite dimensional subspace that is isomorphic (as a Banach space) to a uniformly convex space. I just thought I'd make that clear here, in case someone is watching the page for changes and wishes to object. Hanche 21:24, 3 June 2007 (UTC)[reply]

Here is a good source (containing three correct definitions, with existence and uniqueness ensured): [2]. It also eliminates the need of this mysterious m; sorry, being quite young in 1974 I did not know that this notation for the space of bounded sequences is not at all universally accepted. Boris Tsirelson (talk) 07:49, 18 February 2009 (UTC)[reply]

And another source: [3]. Boris Tsirelson (talk) 10:34, 13 June 2010 (UTC)[reply]

Question

I don't much like the way the space is introduced: the unit ball of c₀ satisfies 1-4, so what? You have to wait "weakly compact", somewhat hidden outside what seems to be the main point, to get to the real thing.

Why not say that A is the "smallest" such set? Bdmy (talk) 08:18, 12 April 2013 (UTC)[reply]

Yes, indeed! The smallest such set is exactly the definition. Clearly, this article was written by careless non-experts. Boris Tsirelson (talk) 10:02, 12 April 2013 (UTC)[reply]

Ah! I see that you make a point not to edit this article yourself !!! Anonymous best regards, Bdmy (talk) 10:46, 12 April 2013 (UTC)[reply]

For two reasons. First, it is not a good idea, to write here about oneself. Second, if the only editor that wish and can to describe a topic here is the author then probably the topic is not worth to be described here. Boris Tsirelson (talk) 11:58, 12 April 2013 (UTC)[reply]