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.