The tensor product of weights
Yoshikazu Katayama · Proceedings of the Japan Academy Series A Mathematical Sciences · 1974
1. Introduction.The tensor product of normal semi-finite weights on von Neumann algebras was defined and used by several authors, e.g.F.Combes [3], A. Connes [6].It was defined so that the resulting weight has favorable properties.Here in this note, we shall make a study on other possible definitions.We then establish a Radon- Nikodym type theorem for the tensor product of weights.The author wishes to thank Professors O. Takenouchi and S. Kitagawa for their helpful suggestions.2. The tensor product of normal semi.finiteweights.Given a weight p on avon Neumann algebra M, we denote by m the *-subalgebra spanned by n*n where n= {x in M (x*x) + c}.The linear extension on m of l()+ will be denoted by .The following is the key lemma