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representation of a Cc(G)*- topological algebra (Definition)
Definition 0.1   A representation of a $C_c({\mathsf{G}})$ topological $*$–algebra is defined as a continuous $*$–morphism from $C_c({\mathsf{G}})$ to $B(\H )$, where ${\mathsf{G}}$ is a topological groupoid, (usually a locally compact groupoid, ${\mathsf{G}}_{lc}$), $\H$ is a Hilbert spacehttp://physicslibrary.org/encyclopedia/NormInducedByInnerProduct.html, and $B(\H )$ is the $C^*$-algebra of bounded linear operators on the Hilbert space $\H$; of course, one considers the inductive limit (strong) topology to be defined on $C_c({\mathsf{G}})$, and then also an operator weak topology to be defined on $B(\H )$.



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Keywords:  representation, groupoid C*-algebra

Cross-references: operator, linear operators, Hilbert space, locally compact groupoid, topological groupoid, topological, representation

This is version 1 of representation of a Cc(G)*- topological algebra, born on 2009-05-09.
Object id is 738, canonical name is RepresentationOfACcGTopologicalAlgebra.
Accessed 234 times total.

Classification:
Physics Classification: 00. (GENERAL)
 02. (Mathematical methods in physics)
 03. (Quantum mechanics, field theories, and special relativity )
 03.65.Fd (Algebraic methods )
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