A Banach space \((V,||~||)\), in which the norm \([||~||"\) is given by the square root \[||~||:=\sqrt{\langle\cdot,\cdot\rangle},\] where \(\langle\cdot,\cdot\rangle\) is a positive definite dot product is called a Hilbert space, named after the German mathematician David Hilbert (1862 - 1943).
