Banach algebra

Particular kind of algebraic structure

In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A {\displaystyle A} over the real or complex numbers (or over a non-Archimedean complete normed field) that at the same time is also a Banach space, that is, a normed space that is complete in the metric induced by the norm. The norm is required to satisfy ‖ x y ‖ ≤ ‖ x ‖ ‖ y ‖ for all x , y ∈ A . {\displaystyle \|x\,y\|\ \leq \|x\|\,\|y\|\quad {\text{ for all }}x,y\in A.} This ensures that the multiplication operation is conti...