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Math Help - Spectral radius (Banach algebra)

  1. #1
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    Spectral radius (Banach algebra)

    Hi everyone,

    I would like to ask for some help about the following problem:

    "A is a Banach algebra on Hilbert space with unitary element. Prove that the following property stand for the spectral radius (r):

    r(x y) =r (x y) where x and y are elements of the A Banach algebra."


    Thanks in advance
    Johan
    Thanks from girdav
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  2. #2
    Super Member girdav's Avatar
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    Re: Spectral radius (Banach algebra)

    Do you mean r(xy)=r(yx)? Use the formula r(a)=\lim_{n\to\infty}\lVert a^n\rVert^{1/n}$ and (yx)^n=y(xy)^{n-1}x.
    Last edited by girdav; March 4th 2012 at 12:28 PM. Reason: fixed tex.
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    Re: Spectral radius (Banach algebra)

    Thanks girdav for quick reply
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