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Hilbert space is a [[inner product space]] that is also a [[complete metric space]].  A Hilbert space is always a [[Banach space]], but the converse need not hold.

Hilbert space is a [[inner product space]] that is also a [[complete metric space]].  A Hilbert space is always a [[Banach space]], but the converse need not hold. Hilbert space is named after mathematician [[David Hilbert]], whom used it to provide a natural context in which to generalize the concept of [[Fourier series]] and [[Fourier Transformation]] in terms of arbitrary orthogonal functions defined on infinite dimensional inner product space.

 

[[Category:Mathematics]]

[[Category:Mathematics]]