is a Japanese mathematician.

Life

Sakai studied mathematics at the Tohoku University (Sendai). He there received the B. A. degree in 1953 and a doctorate at the same University in 1961. From 1960 to 1964, he was a faculty member of

Waseda University , mottoeng = Independence of scholarship , established = 21 October 1882 , type = Private , endowment = , president = Aiji Tanaka , city = Shinjuku , state = Tokyo , country = Japan , students = 47,959 , undergrad = 39,382 , postgrad ...

. He then went to the

University of Pennsylvania The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universit ...

, where he became a professor in 1966 and remained until 1979. He then returned to Japan and went to the

Nihon University , abbreviated as , is a private research university in Japan. Its predecessor, Nihon Law School (currently the Department of Law), was founded by Yamada Akiyoshi, the Minister of Justice, in 1889. It is one of Japan's leading private univers ...

. In 1992, he received the

Japanese Mathematical Society Autumn Prize Japanese may refer to: * Something from or related to Japan, an island country in East Asia * Japanese language, spoken mainly in Japan * Japanese people, the ethnic group that identifies with Japan through ancestry or culture ** Japanese dias ...

. He is a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings ...

. Sakai's main field is

functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined ...

and

mathematical physics Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and t ...

. 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 (cf. a

theorem of Kadison-Sakai In mathematics, a theorem is a statement that has been proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of th ...

.)George A. Elliot: ''On derivations of AW*-algebras'', Tóhoku Mathematical Journal, Band 30 (1978), Seiten 263–276.

Works

*''C *-algebras and W *-algebras'', Springer-Verlag 1971, Ergebnisse der Mathematik und ihrer Grenzgebiete, Volume 60, (republished in 1998 in ''Classics in Mathematics'') *''Operator algebras in dynamical systems, the theory of unbounded derivations in C*-algebras,'' Cambridge University Press (1991),

References

{{DEFAULTSORT:Sakai, Shoichiro 1928 births Living people 20th-century Japanese mathematicians 21st-century Japanese mathematicians Fellows of the American Mathematical Society Functional analysts Academic staff of Waseda University University of Pennsylvania faculty