They are Hilbert spaces if they obey the parallelogram identity and the inner product that defines it as a Hilbert space is given by the polarization identity.
Both the Fr?het derivative and the G?eaux derivative are analogous versions of the derivative from differential calculus defined on these, and a non-separable polynomially reflexive subclass of them is named for Tsirelson. The space of continous functions defined on a closed interval that map to an n-dimensional Euclidean space is one of these, as are the sets of real and complex numbers. They are Hilbert spaces if they obey the parallelogram identity and the inner product that defines it as a Hilbert space is given by the polarization identity. FTP, name these spaces, one of the central objects of study in functional analysis, which are defined as being complete normed vector spaces and are named for a Polish mathematician.
Both the Fr?het derivative and the G?eaux derivative are analogous versions of the derivative from differential calculus defined on these, and a non-separable polynomially reflexive subclass of them is named for Tsirelson.
Banach spaces