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  Volume 10, Issue 1, Article 4
 
Clarkson-McCarthy Interpolated Inequalities in Finsler Norms
    Authors: Cristian Conde,  
    Keywords: p-Schatten class, Complex method, Clarkson-McCarthy inequalities.  
    Date Received: 29/08/08  
    Date Accepted: 14/01/09  
    Subject Codes:

Pri: 46B70, 47A30; Sec: 46B20, 47B10.

  
    Editors: Rajendra Bhatia,  
 
    Abstract:

We apply the complex interpolation method to prove that, given two spaces $ B^{(n)}_{p_0,a;s_0},$ $ B^{(n)}_{p _1,b;s_1}$ of $ n$-tuples of operators in the $ p$-Schatten class of a Hilbert space $ H$, endowed with weighted norms associated to positive and invertible operators $ a$ and $ b$ of $ B(H)$ then, the curve of interpolation $ (B^{(n)} _{p_0,a;s_0} , B^{(n)}_{p_1,b;s_1})_{[t]}$ of the pair is given by the space of $ n$-tuples of operators in the $ p_t$-Schatten class of $ H$, with the weighted norm associated to the positive invertible element $ gamma_{a,b}(t)=a^{1/2}(a^{-1/2}b a^{-1/2})^t a^{1/2}$.

         
       
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