Schauderbasised
Schauderbasised is a term used to describe a theoretical framework within functional analysis, a branch of mathematics. It specifically refers to the concept of a Schauder basis in a Banach space. A Schauder basis for a Banach space X is a sequence of vectors {e_n} such that every vector x in X can be uniquely represented as an infinite linear combination of these basis vectors, i.e., x = sum_{n=1 to infinity} c_n e_n, where the coefficients c_n are scalars. The convergence of this sum is understood in the norm of the Banach space.
The existence and properties of Schauder bases are crucial in understanding the structure of Banach spaces.