Abstract
Let V:1,…,Vm be inner product spaces, and let L be a linear transformation on V1 ⊗…⊗Vm which satisfies (Lz,z)=0 for every decomposable tensor z. It is known that if the field is the complex numbers, then (Lz,z)=0 for every z. This paper contains a short proof of this result, an extension of it to arbitrary symmetry classes of tensors, and an analysis of its failure when the field is the real numbers.
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