equivalence of definitions of -algebra
A Banach algebra with an antilinear involution such that for all is a -algebra.
It follows from the product inequality that
Therefore, . Putting for , we also have . Thus, the involution is an isometry: . So now,
Hence, . ∎
A Banach algebra with an antilinear involution such that is a -algebra.
|Title||equivalence of definitions of -algebra|
|Date of creation||2013-03-22 17:42:27|
|Last modified on||2013-03-22 17:42:27|
|Last modified by||rspuzio (6075)|