Square-cube law: Difference between revisions

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'''[[Mark Naimark|Naimark]]'s Problem''' is a question in [[functional analysis]]. It asks whether every [[C*-algebra]] that has only one [[irreducible representation|irreducible <math> * </math>-representation]] up to [[Self-adjoint operator#Spectral theorem|unitary equivalence]] is [[isomorphic]] to the <math> * </math>-algebra of [[Compact operator on Hilbert space|compact operator]]s on some (not necessarily separable) [[Hilbert space]].
== or some of the slaves purchased from other planets ==


The problem has been solved in the affirmative for special cases (specifically for separable and Type-I C*-algebras). {{harvtxt|Akemann|Weaver|2004}} used the [[diamond principle|<math> \diamondsuit </math>-Principle]] to construct a [[C*-algebra]] with <math> \aleph_{1} </math> generators that serves as a counterexample to Naimark's Problem. More precisely, they showed that the statement "'''There exists a counterexample to Naimark's Problem that is generated by [[Aleph One|<math> \aleph_{1} </math>]] elements'''" is <u>independent</u> of the axioms of [[Zermelo-Fraenkel set theory|Zermelo-Fraenkel Set Theory]] and the [[axiom of choice|Axiom of Choice]] (<math> \mathsf{ZFC} </math>).
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相关的主题文章：
==See also==
<ul>
*[[List of statements undecidable in ZFC|List of statements undecidable in <math> \mathsf{ZFC} </math>]]
 
*[[Gelfand–Naimark theorem|Gelfand-Naimark Theorem]]
  <li>[http://www.aigfa.org/forum/front_slider/forum/item/create_form/1 http://www.aigfa.org/forum/front_slider/forum/item/create_form/1]</li>
 
 
==External links==
  <li>[http://forum.vuilen.com/showthread.php?p=2739718#post2739718 http://forum.vuilen.com/showthread.php?p=2739718#post2739718]</li>
*{{Citation | last1 = Akemann | first1 = Charles | last2 = Weaver | first2 = Nik | title = Consistency of a counterexample to Naimark's problem | doi = 10.1073/pnas.0401489101 | mr = 2057719 | year = 2004 | journal = [[Proceedings of the National Academy of Sciences|Proceedings of the National Academy of Sciences of the United States of America]] | volume = 101 | issue = 20 | pages = 7522–7525 | arxiv = math.OA/0312135}}
 
 
  <li>[http://cm.jesperlaursen.com/displayimage.php?pid=415/displayimage.php?pid=415&message_id=bacb5675d8bf3ce26777700b652544a3&message_icon=info#cpgMessageBlock http://cm.jesperlaursen.com/displayimage.php?pid=415/displayimage.php?pid=415&message_id=bacb5675d8bf3ce26777700b652544a3&message_icon=info#cpgMessageBlock]</li>
[[Category:Conjectures]]
 
[[Category:C*-algebras]]
</ul>
[[Category:Independence results]]
 
 
{{Mathanalysis-stub}}

Revision as of 14:51, 10 February 2014

or some of the slaves purchased from other planets

His place is intact.

'to your face, you are shameless.' Nightmare candle ルイヴィトン 帽子 looked Luo Feng Wang sneer, 'that ベルト ルイヴィトン we will go to shameless play!'

Boom!

powerful force instantly immortal shackled Dylan, Luo Feng, while one of the world's power to spread out in all directions, the moment will be to wrap the ルイヴィトン 新作 2014 entire planet.

'closed!' Nightmare candle king cold complexion.
On
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so the moment ......

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Luo Feng looking for a change, 相关的主题文章：

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