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Homework Help: Spectrum, banach algebra

  1. May 9, 2010 #1
    1. The problem statement, all variables and given/known data

    How to show element of finite dimensional banach algebra has finite spectrum?

    2. Relevant equations

    spectrum(x) = set of complex numbers 'c' with cI-x not invertible, I is identity

    3. The attempt at a solution

    please help to start, I dont know
  2. jcsd
  3. May 9, 2010 #2


    Staff: Mentor

    According to the rules of this forum, you have to show an effort at solving this before we can provide help.
  4. May 9, 2010 #3


    User Avatar
    Science Advisor
    Homework Helper

    Try showing that the eigenvalues belonging to different elements of the spectrum are linearly independent.
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