Abstract

An m- linear operator T on a normed vector space V shall be called multiplicative if ▪ N being the given norm. Similarly, we shall say that T is Jordan-multiplicative if ▪ where S m denotes the symmetric group on m elements. Our purpose is to provide necessary and sufficient conditions for the multiplicativity and the Jordan-multiplicativity of T, when V is finite dimensional and N is a weighted l 1 norm. The results obtained in this note generalize some of those in [1] where V was an associative algebra and the multilinear operation was simply the product of m vectors.

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