B are one of the tools and objects of study in functional analysis and are used in some formulations of quantum mechanics. A B^{*}-algebras^{*}-algebra A is a Banach algebra over the field of complex numbers, together with a map ^{*} : A -> A called involution which has the follow properties: |

B are mathematical structures studied in functional analysis. A B^{*}-algebras^{*}-algebra A is a Banach algebra over the field of complex numbers, together with a map ^{*} : A -> A called involution which has the follow properties: |

if the property is also true, the algebra is actually a '''C^{*}-algebra'''. |

If the following property is also true, the algebra is actually a '''C^{*}-algebra''': |