Sakai studied mathematics at the Tohoku University (Sendai).
In 1992, he received the Japanese Mathematical Society Autumn Prize.
[2] Sakai's main field is functional analysis and mathematical physics.
His textbook published in the Springer series in C *-algebras and W *-algebras, in which W *-algebras as C *-algebras are introduced with a predual, is widely used.
That fact the W *-algebras may be defined in this way is known as a theorem of Sakai[3] (cf.