Timeline for Reference needed for: every idempotent in a C*-algebra is similar to a hermitian one
Current License: CC BY-SA 2.5
10 events
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| Mar 30, 2010 at 3:30 | comment | added | Jonas Meyer | A remark on the minimalist approach in Kaplansky's Rings of operators: Gelfand and Naimark initially took as an axiom for abstract C*-algebras that 1 + x*x is invertible for all x. It was 17 years before this was shown to follow from the other axioms, even though G & N believed it did from the start. | |
| Mar 9, 2010 at 22:30 | comment | added | Yemon Choi | Thanks Jonas for the continued efforts. I think the Kaplansky references are the closest to what I was looking for (and the place where I first saw this result quoted without proof was a short article by Montgomery, based on ... something in Kaplansky's Fields and Rings). | |
| Mar 9, 2010 at 22:28 | vote | accept | Yemon Choi | ||
| Mar 9, 2010 at 22:16 | history | edited | Jonas Meyer | CC BY-SA 2.5 |
Added older Kaplansky reference
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| Mar 3, 2010 at 7:12 | history | edited | Jonas Meyer | CC BY-SA 2.5 |
mostly add formula for projection
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| Mar 3, 2010 at 4:38 | history | edited | Jonas Meyer | CC BY-SA 2.5 |
Added Kaplansky reference; added 53 characters in body; deleted 1 characters in body
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| Mar 3, 2010 at 3:26 | comment | added | Jonas Meyer | I don't know such a source. I've seen the same sketch you provided, but I also don't have any standard reference for that. I'll be curious to see what turns up. I understand your desire for a more general source. While K-theory is a good place to look for results about equivalence of idempotents (now that the subject exists), it does seem a bit much for just this result. Of course, no K-theory is actually used in the proofs I linked to! | |
| Mar 3, 2010 at 3:08 | comment | added | Yemon Choi | Thanks - either of those references would do, although I would still prefer a more general and less specialist source. (To give some background: I first saw it, stated without proof, in a short Bull. AMS paper from the 1950s, so it predates K-theory of C*-algebras by a long way...) | |
| Mar 3, 2010 at 2:55 | history | edited | Jonas Meyer | CC BY-SA 2.5 |
Added second reference
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| Mar 3, 2010 at 2:26 | history | answered | Jonas Meyer | CC BY-SA 2.5 |