Talk:C*-algebra

message: What is the point of the spaces introduced by User:Deflog, some of which change the paragraph structure?CSTAR 19:36, 14 May 2004 (UTC)
replies: text: Yes it does.  Indeed, this is the commonly accepted definition. Cf Dixmier 1.2.1 CSTAR 23:56, 3 Aug 2004 (UTC)
replies: text: According to Blackadar, Operator Algebras, II.1.1.2, "in many older references, abstract C*-algebras were called B*-algebras, with the name C*-algebra reserved for concrete C*-algebras".
The "history" section is unclear. It seems to be saying that B* <==> C* but the ==> part is easier to prove and the <== part need not use ||x*||=||x||. However I fail to see what "For these reasons ..." actually means.  — Preceding unsigned comment added by 192.76.7.215 (talk) 14:51, 26 September 2013 (UTC)
thread_title: Comment

message: This is currently a redirect page. Please voice objections soon. VERY soon. CSTAR 04:25, 8 Sep 2004 (UTC)
thread_title:  Moving to [[C*-algebra]] 

message: I have changed the statement 'A is type I iff every factor representation generates a type I factor' to 'A is type I iff every representation generates a type I von Neumann algebra'. If I'm not mistaken, the latter is equivalent with the former (or is a separability condition necessary?)? I get my definition (indirectly) from Arveson's book. So I'll add the first statement as a relaxation of the type I condition. I think this approach is nicer, since then the definition is easier and more general to state.
: They are clearly equivalent for separable A. According to Sakai's book, Theorem 4.6.4 it's true in general.--CSTAR 04:52, 16 September 2006 (UTC)
thread_title:  type I C*-algebras 

message: I don't think it's just the grammar that's incorrect in this sentence: "Furthermore, a *-homomorphism between C*-algebras is isometry."  Should that be a *-isomorphism? 76.126.116.54 (talk) 04:03, 12 March 2009 (UTC)
replies: text: Maybe I should stop being a baby, look up the correct statement and fix it myself.  Missing that teeny word "injective", according to Davidson, C*-algebras by Example, Theorem I.5.5. 76.126.116.54 (talk) 04:09, 12 March 2009 (UTC)
thread_title:  All homomorphisms are isometries? 

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thread_title:  Copyright problem removed 

message: WP:DICDEF: †-algebra is apparently an alternative name for a finite C*-algebra. QVVERTYVS (hm?) 08:50, 16 July 2015 (UTC)
thread_title:  Proposed merge with [[†-algebra]] 

message: In the lede it says a C* algebra is an algebra of operators on a Hilbert space. This is not supported by the text, which gives an abstract definition as a kind of Banach algebra. These should be brought into line. 84.226.79.103 (talk) 11:13, 1 March 2018 (UTC)
thread_title:  Introduction versus body. Abstract characterization versus operators on a Hilbert space.