Von Neumann Algebras
In the context of functional analysis and operator algebras, representation refers to a way of expressing algebraic structures through linear transformations on a vector space. This concept is crucial for connecting abstract algebraic ideas with concrete mathematical objects, allowing one to study properties of algebras via their actions on spaces. It's particularly significant as it underlies the GNS construction, helps characterize von Neumann algebras as dual spaces, and is also relevant in theoretical physics scenarios like string theory.
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