A Banach algebra is a type of algebraic structure that combines the properties of a normed space and an algebra. In a Banach algebra, elements can be added and multiplied, and there is a way to measure their size or distance using a norm. This structure allows for the study of linear operators and functions in a rigorous mathematical framework. One key feature of Banach algebras is that they are complete, meaning that any Cauchy sequence of elements in the algebra converges to an element within the same algebra. This completeness property is essential for many applications in functional analysis and helps in understanding the behavior of linear operators and functional equations.