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)Bp1 ,b;s1 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(n)(n)of interpolation (Bp0 ,a;s0 , Bp1 ,b;s1 )[t] of the pair is given by the space of n-tuples of operators inthe pt -Schatten class of H, with the weighted norm associated to the positive invertible elementγa,b (t) = a1/2 (a−1/2 ba−1/2 )t a1/2 .