Banach Algebra
- Pure Mathematics -
Algebra Dictionary
Definition
A Banach algebra is an algebra A over the real or complex numbers that is also a Banach space for a norm ||·|| satisfying ||xy|| ≤ ||x|| · ||y|| for all x,y in A and such that A is complete in that norm. The algebra may be unital or nonunital; continuity of multiplication is built into the norm inequality.