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.
Read more about this topic: Quotient Space (linear Algebra)
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“With sturdy shoulders, space stands opposing all its weight to nothingness. Where space is, there is being.”
—Friedrich Nietzsche (1844–1900)