Timeline for injectivity of Fourier transform: is there algebraic proof?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Nov 22, 2012 at 9:49 | comment | added | Yemon Choi | @Dmitri: Banach-star algebras need not be semisimple, and can have rather unpleasant properties in general | |
| Nov 8, 2012 at 8:57 | comment | added | Fedor Petrov | @Dmitri. It is, but this star does not make it C*-algebra (since $\|ff^{*}\|\ne \|f\|^2$ in general). | |
| Nov 4, 2012 at 18:09 | comment | added | Dmitri Pavlov | L^1(G) is a Banach *-algebra, see planetmath.org/encyclopedia/GroupAlgebra2.html or en.wikipedia.org/wiki/… | |
| Oct 17, 2011 at 5:39 | comment | added | Fedor Petrov | @Christopher: the goal is rather not avoiding any theory, but understanding this fact in Banach algebras context. For example, unital $C^{*}$-algebras are semisimple, but this algebra does not seem to have star (or am I blind here?). But maybe some Banach algebras with clear algebraic property or additional structure are also always semisimple, and $A$ is in this class by not so hard to check reasons. | |
| Oct 17, 2011 at 3:59 | comment | added | Christopher A. Wong | Could you clarify exactly what results/theory/tools you are trying to avoid using? | |
| Oct 16, 2011 at 12:44 | history | edited | KConrad | CC BY-SA 3.0 |
added 57 characters in body
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| Oct 16, 2011 at 11:22 | history | edited | Fedor Petrov | CC BY-SA 3.0 |
edited title
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| Oct 16, 2011 at 9:45 | history | asked | Fedor Petrov | CC BY-SA 3.0 |