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Acta Mathematica Vietnamica

STRONG MINIMALITY OF GAUSSIAN-SUMMING NORM

V. TARIELADZE, R. VIDAL

Abstract

By means of a sequence φ:=(φn)nN of square-integrable functions a notion of a φ-summing operator is defined. It is shown that if infnφn2>0, then any φ-summing operator is Gaussian-summing. This recovers a previously known result, which asserts the same in case when φ:=(φn)nN is an orthonormal sequence.