Quotient Space (linear Algebra) - Quotient of A Banach Space By A Subspace

Quotient of A Banach Space By A Subspace

If X is a Banach space and M is a closed subspace of X, then the quotient X/M is again a Banach space. The quotient space is already endowed with a vector space structure by the construction of the previous section. We define a norm on X/M by

The quotient space X/M is complete with respect to the norm, so it is a Banach space.