C*-algebra
Sign in to saveAlso known as B*-algebra, †-algebra
In mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties of the adjoint. A particular case is that of a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties:
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Article
17 sectionsContents
- Abstract characterization
- History: B*-algebras and C*-algebras
- Structure of C*-algebras
- Self-adjoint elements
- Quotients and approximate identities
- Examples
- Finite-dimensional C*-algebras
- C*-algebras of operators
- C*-algebras of compact operators
- Commutative C*-algebras
- C*-enveloping algebra
- Von Neumann algebras
- Type for C*-algebras
- C*-algebras and quantum field theory
- See also
- Notes
- References
In mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties of the adjoint. A particular case is that of a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties: A is a topologically closed set in the norm topology of operators. A is closed under the operation of taking adjoints of operators.
Another important class of non-Hilbert C*-algebras includes the algebra C_0(X) of complex-valued continuous functions on X that vanish at infinity, where X is a locally compact Hausdorff space.