Clarkson-McCarthy Interpolated Inequalities in Finsler norms

CRISTIAN CONDE

Journal of inequalities in pure and applied mathematics

Victoria University

Lugar: Melbourne; Año: 2009 p. 1 - 10

1443-5756

We apply the complex interpolation method to prove that, given two spaces B(p0 ,a;s0)^(n) and B(p1 ,b;s1)^(n) of n-tuples of operators in the p-Schatten class of a Hilbert space H, endowed withweighted norms associated to positive and invertible operators a and b of B(H) then, the curve of interpolation                                             (B(p0 ,a;s0)^(n) , B(p1 ,b;s1)^(n) )_[t]of the pair is given by the space of n-tuples of operators in the pt-Schatten class of H, with the weighted norm associated to the positive invertible element                                       γ_{a,b} (t) = a^{1/2} (a^{−1/2} ba^{−1/2} )^t a^{1/2} .