Sherman–Takeda theorem
In mathematics, specifically in functional analysis, the Sherman–Takeda theorem states that if A is a C*-algebra then its double dual is a W*-algebra, and is isomorphic to the weak closure of A in the universal representation of A.
The theorem was announced by {{harvtxt|Sherman|1950}} and proved by {{harvtxt|Takeda|1954}}. The double dual of A is called the universal enveloping W*-algebra of A.
References
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- {{Citation | last1=Sherman | first1=S. | title=Proceedings of the International Congress of Mathematicians 1950 | url=https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1950.1/ICM1950.1.ocr.pdf | publisher=American Mathematical Society | location=Providence, R.I. | volume=1 | chapter=The second adjoint of a C* algebra | pages=470|year=1950}}
- {{Citation | last1=Takeda | first1=Zirô | title=Conjugate spaces of operator algebras | url=https://www.jstage.jst.go.jp/article/pjab1945/30/2/30_2_90/_article/-char/en | mr=0063578 | year=1954 | journal=Proceedings of the Japan Academy | issn=0021-4280 | doi=10.3792/pja/1195526177 | volume=30 | issue=2 | pages=90–95| doi-access=free }}
{{Functional analysis}}
{{Spectral theory}}
{{DEFAULTSORT:Sherman-Takeda theorem}}
Category:Theorems in functional analysis
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