Sherman–Takeda theorem
In mathematics, the Sherman–Takeda theorem states that if A is a C* algebra then its double dual is a W* algebra, and any homomorphism of A to a W* algebra factors through its double dual. The theorem was announced by Sherman (1950) and proved by Takeda (1954). The double dual of A is called the universal enveloping W* algebra of A.
References
- Sherman, S. (1950), "The second adjoint of a C* algebra", Proceedings of the International Congress of Mathematicians 1950, 1, Providence, R.I.: American Mathematical Society, pp. 470, http://mathunion.org/ICM/ICM1950.1/
- Takeda, Zirô (1954), "Conjugate spaces of operator algebras", Proceedings of the Japan Academy 30 (2): 90–95, ISSN 0021-4280, MR0063578, http://www.journalarchive.jst.go.jp/english/jnlabstract_en.php?cdjournal=pjab1945&cdvol=30&noissue=2&startpage=90