Operator Algebras Article Index for
Operator
Website Links For
Operator
 

Information About

Operator Algebras




Such algebras can be used to study sets of operators ''simultaneously''. From this point of view, operator algebras can be regarded as a generalization of Spectral Theory of a single operator. In general operator algebras are non-commutative rings.

  • -algebra" class="copylinks">C
    algebra s and Von Neumann Algebra s. C
    algebras can be easily characterized abstractly by a condition relating the norm, involution and multiplication. The Gelfand–Naimark Theorem states that an abstract C
    algebra is always isometrically
    isomorphic to a C
    algebra of operators on a Hilbert space. It is possible to give an abstract characterization of a von Neumann algebra as a C
    algebra with a Predual .


Examples of operator algebras which are not self-adjoint include:



SEE ALSO