Abstract
Let and be fields and let n be a positive integer. Let and be linear spaces over such that and let and be linear spaces over . Let be the tensor product of and and let be the subspace of symmetric tensors of . In this paper, we show that a map satisfies
for all rank r tensors if and only if is additive. Here r is a fixed integer such that and with , or with and . Examples showing the indispensability of assumption in our results are included.
Acknowledgements
The authors are indebted to the referee for a careful reading of the original manuscript and for useful comments and suggestions.
Disclosure statement
No potential conflict of interest was reported by the authors.