has an approximate identity
- has an identity element if and only if is discrete.
When is discrete the identity element of is just the Dirac delta, i.e. the function that takes the value on the identity element of and vanishes everywhere else.
Nevertheless, has always an approximate identity.
Theorem - has an approximate identity . Moreover the approximate identity can be chosen to the following :
is self-adjoint (http://planetmath.org/InvolutaryRing),
where stands for the space of continuous functions with compact support.
|Title||has an approximate identity|
|Date of creation||2013-03-22 17:42:40|
|Last modified on||2013-03-22 17:42:40|
|Last modified by||asteroid (17536)|
|Defines||has an identity element iff is discrete|