Timeline for Gelfand representation and functional calculus applications beyond Functional Analysis
Current License: CC BY-SA 3.0
3 events
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| Apr 23, 2013 at 13:24 | comment | added | jbc | My understanding of the proof is that Carleson demonstrated the validity of the interpolation property with hard analysis (which, by the way, led to the important concept of Carleson measures). The Banach algebra bit, i.e., the proof of the equivalence of this with the denseness (which is apparently due to Newman), uses the fact that the Gelfand-Neumark transform allows one to consider bounded analytic functions on the open disc and their absolute values as continuous functions on a compactum, the point being that such functions attain their infimum. | |
| Apr 22, 2013 at 15:56 | comment | added | Julien | That's a good example. Thank you. Apart from the spectrum interpretation of the result, do Carleson's proof, or Wolff's proof, actually use the Gelfand transform? | |
| Apr 22, 2013 at 6:38 | history | answered | jbc | CC BY-SA 3.0 |