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C^*-Algebra Representation

A representation of a C^*-algebra A is a pair (H,phi) where H is a Hilbert space and phi:A->B(H) is a *-homomorphism. (H,phi) is said to be faithful if phi is injective.

For example, if H is a Hilbert space and A is a C^*-subalgebra of B(H), then (H,iota) where iota is the inclusion map is a faithful representation.

This entry contributed by Mohammad Sal Moslehian

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References

Murphy, G. J. C-*-Algebras and Operator Theory. New York: Academic Press, 1990.

Cite this as:

Moslehian, Mohammad Sal. "C^*-Algebra Representation." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/C-Star-AlgebraRepresentation.html

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