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A Characterization of C*-normed Algebras via Positive Functionals
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- Journal:
- Canadian Mathematical Bulletin / Volume 61 / Issue 1 / 01 March 2018
- Published online by Cambridge University Press:
- 20 November 2018, pp. 114-123
- Print publication:
- 01 March 2018
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- Article
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We give a characterization of
${{C}^{*}}$-normed algebras, among certain involutive normed ones. This is done through the existence of enough specific positive functionals. The same question is also examined in some non normed (topological) algebras.
THE NON-COMMUTATIVE SCHWARTZ SPACE IS WEAKLY AMENABLE
- Part of
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- Journal:
- Glasgow Mathematical Journal / Volume 59 / Issue 2 / May 2017
- Published online by Cambridge University Press:
- 10 June 2016, pp. 437-443
- Print publication:
- May 2017
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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
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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.
