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| ``Re: Banach *-algebra representation remark''
by bci1 on 2008-09-20 22:07:42 |
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| | The representations of both Banach *-algebra and groups are defined with the target space selected as a Hilbert space-- whose definition also involves a Banach space; in the case of Banach *-algebras one has an underlying Banach space in the definition of the Banach *-algebra. Thus, one can define forgetful functors that `forget' the added structure to the Banach space; there is therefore a mapping, or morphism, underlying the representation which is a homeomorphism of Banach spaces. Such forgetful functors also have right adjoint functors that operate in `reverse'. The definition of Banach *-algebra representations thus would suggest the existence of a representable functor with the source being the category of Banach *-algebras. |
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