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DERIVATIONS OF FRÉCHET NUCLEAR GB
$^{\ast }$-ALGEBRAS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 92 / Issue 2 / October 2015
- Published online by Cambridge University Press:
- 04 June 2015, pp. 290-301
- Print publication:
- October 2015
-
- Article
-
- You have access
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It is an open question whether every derivation of a Fréchet GB
$^{\ast }$-algebra 
$A[{\it\tau}]$ is continuous. We give an affirmative answer for the case where 
$A[{\it\tau}]$ is a smooth Fréchet nuclear GB
$^{\ast }$-algebra. Motivated by this result, we give examples of smooth Fréchet nuclear GB
$^{\ast }$-algebras which are not pro-C
$^{\ast }$-algebras.
