Proof : Let denote the unit of .
Let and be its spectrum. It is known that the spectrum is a non-empty set (http://planetmath.org/SpectrumIsANonEmptyCompactSet) in .
Let . Since is not invertible and is a division algebra, we must have and so
Let be defined by .
It is clear that is an injective algebra homomorphism.
By the above discussion, is also surjective.
It is isometric because
Therefore, is isometrically isomorphic to .
|Date of creation||2013-03-22 17:29:03|
|Last modified on||2013-03-22 17:29:03|
|Last modified by||asteroid (17536)|