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If an algebra $A$ is a semidirect product of a subalgebra $B$ and an ideal $I$. Is characterized the character space of $A$ by character space of $B$ and character space of $I$?

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  • $\begingroup$ Am I correct in guessing that words like "character amenability" and "module extension Banach algebra" are lurking in the background to your question? $\endgroup$
    – Yemon Choi
    Mar 12, 2013 at 21:31
  • $\begingroup$ My guess is that the solution should not be too difficult and is the sort of thing that people in the past were happy to rediscover as and when they needed it. Why don't you tell us how far you have got at the moment? $\endgroup$
    – Yemon Choi
    Mar 12, 2013 at 21:34
  • $\begingroup$ I think that the spectrum space of the semidirect product of a subalgebra B and an closed two sided ideal I of a Banach algebra A is $\sigma(B)union{0}×\sigma(I)union {0}. I proved one direction and I haven't proved the other direction $\endgroup$
    – Ali
    Mar 12, 2013 at 22:15
  • $\begingroup$ Assuming you are a student, what does your supervisor say? $\endgroup$
    – Yemon Choi
    Mar 14, 2013 at 19:00
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    $\begingroup$ Ali, why on earth not? That is what a supervisor is for $\endgroup$
    – Yemon Choi
    Mar 14, 2013 at 23:31

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