STRONG MINIMALITY OF GAUSSIAN-SUMMING NORM

V. Tarieladze and R. Vidal

Abstract

           By means of a sequence φ. := (φ_n )_{n∈ N} of square-integrable functions a notion of a φ.-summing operator is defined. It is shown that if inf_n||φ_n||₂ > 0, then any φ.-summing operator is Gaussian-summing. This recovers a previously known result, which asserts the same in case when φ. := (φ_n )_{n∈ N} is an orthonormal sequence.