Quadratic integrals and factorization of linear operators

Blower, Gordon (1997) Quadratic integrals and factorization of linear operators. Journal of the London Mathematical Society, 56 (2). pp. 333-346. ISSN 0024-6107

Abstract

We consider operators on the matrix-valued disc algebra. We show that any bounded linear operator T: A ⊗̄ script K → X to a Banach space X of cotype 2 induces a bounded operator Gv → X defined on some weighted Bergman space Gv on the unit disc. We give sufficient conditions on the weight v for the formal inclusion A ⊗̄ script K → Gv, to be 2-C*-summing. Decompositions of T with respect to operator-valued measures are obtained.