One of the most interesting questions in the operator space
theory was ``What are the possible operator algebra products a given
operator space can be equipped with?''. In my Ph.D. thesis, I answered
this question using quasi-multipliers and the Haagerup tensor product.
Quasi-multipliers of operator spaces were defined by Paulsen in late
2002 as natural variations of one-sided multipliers of operator spaces
which had been introduced by Blecher around 1999. However, the
significant relation between quasi-multipliers and operator algebra
products was discovered and proved by myself in early 2003. Since many
people seem to be interested in this topic, in my talk I present this
theorem as well as more recent results in a self-contained manner from
basic definitions with examples. So mathematicians in any fields
(especially, pure algebra) and graduate students are welcomed to attend.