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Its an honour to have you comment. Articles in
Knowledge 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
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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
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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
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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
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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.
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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.
262:. 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.)
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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.
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Tsirelson's paper. There, he apparently uses m for an arbitrary sequence space, but quickly specialises to
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I went and did a little editing: There was a mysterious, undefined m in the definition. I replaced it with
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Here is a good source (containing three correct definitions, with existence and uniqueness ensured):
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on
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such set is exactly the definition. Clearly, this article was written by careless non-experts.
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Ah! I see that you make a point not to edit this article yourself !!! Anonymous best regards,
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4. More than 100 such references are collected on the relevant page of my site, here:
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I don't much like the way the space is introduced: the unit ball of c
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someone is watching the page for changes and wishes to object.
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Gowers: A metamathematical question in Banach space theory
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Oy. Whatever anonymous person who edited the entry on
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Maybe, an external link to it could be appropriate.
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