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 operator topology, weak closure of ''A'' in the universal representation (C*-algebra), universal representation of ''A''. The theorem was announced by and proved by . The double dual of ''A'' is called the universal enveloping W*-algebra of ''A''. References

* * Banach algebras C*-algebras Theorems in functional analysis Operator theory Von Neumann algebras {{Mathanalysis-stub ...
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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 (for example, Inner product space#Definition, inner product, Norm (mathematics)#Definition, norm, or Topological space#Definitions, topology) and the linear transformation, linear functions defined on these spaces and suitably respecting these structures. The historical roots of functional analysis lie in the study of function space, spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining, for example, continuous function, continuous or unitary operator, unitary operators between function spaces. This point of view turned out to be particularly useful for the study of differential equations, differential and integral equations. The usage of the word ''functional (mathematics), functional'' as a noun goes back to the calculus of v ...
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