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  Volume 7, Issue 3, Article 82
 
Spectral Dominance and Young's Inequality in Type III Factors
    Authors: S. Mahmoud Manjegani,  
    Keywords: Operator inequality, Young's inequality, Spectral dominance, Type III factor.  
    Date Received: 15/12/05  
    Date Accepted: 25/04/06  
    Subject Codes:

Pri: 47A63; Sec: 46L05.

  
    Editors: Huzihiro Araki,  
 
    Abstract:

Let $ p, q> 0$ satisfy $ frac{1}{p}+frac{1}{q}=1$. We prove that for any positive invertible operators $ a$ and $ b$ in $ sigma$-finite type III factors acting on Hilbert spaces, there is a unitary $ u$, depending on $ a$ and $ b$ such that

$displaystyle u^*vert abvert u le frac{1}{p}a^p+frac{1}{q}b^q .$

         
       
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