Timeline for A Banach or $C^*$ algebraic analogy of a classical fact in real analysis
Current License: CC BY-SA 4.0
12 events
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| Apr 25, 2019 at 6:09 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| Apr 25, 2019 at 6:08 | comment | added | Ali Taghavi | @YemonChoi so it remains to consider the question for noncommutative algebras and their irreducible representation. | |
| Apr 23, 2019 at 15:05 | comment | added | Ali Taghavi | @Ruy yes that is an interesting Idea. | |
| Apr 23, 2019 at 11:00 | comment | added | Ali Taghavi | @YemonChoi So I understand my question for commutative case is trivial since the range of $D$ is contained in the kernel of all character. Thanks for your help. | |
| Apr 22, 2019 at 23:39 | comment | added | Ruy | It might be more interesting to consider a densely defined derivation. | |
| Apr 22, 2019 at 21:18 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| Apr 22, 2019 at 21:17 | comment | added | Ali Taghavi | Yes at the first part I mean commutative Banach algebras. | |
| Apr 22, 2019 at 21:16 | comment | added | Ali Taghavi | @YemonChoi Very helpful comments | |
| Apr 22, 2019 at 21:02 | comment | added | Yemon Choi | Finally: as soon as you are considering derivations from a commutative Banach algebra to itself, you should always have in mind the Singer-Wermer theorem (this can be found in the book of Bonsall-Duncan, or in the book of Dales) | |
| Apr 22, 2019 at 21:00 | comment | added | Yemon Choi | In your second paragraph, you are trying to deduce behaviour of the iterates of $D$ from information defined in terms of the characters of $A$. What do you intend to do in cases where $A$ has a large Jacobson radical (which in the commutative case is the intersection of the kernels of characters) | |
| Apr 22, 2019 at 20:59 | comment | added | Yemon Choi | In the first part of your question, with a general Banach algebra, are you assuming it is commutative? Because if not, the maximal ideal space could be empty. | |
| Apr 22, 2019 at 20:53 | history | asked | Ali Taghavi | CC BY-SA 4.0 |