Quasi-multiplies and algebrizations of an operator space

Abstract

One of the most interesting questions in the theory of operator spaces was: What are the possible operator algebra products a given operator space can be equipped with? The author answered the question using quasi-multipliers defined in. That is, the operator algebra products a given operator space can be equipped with are precisely the bilinear mappings implemented by contractive quasi-multipliers. Futhermore, the operator algebra products were characterized in terms of matrix norms with the Haagerup tensor product. This result is remarkable in the sense that an algebraic properly (products) is deduced from a geometric property.