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Banach space a normed vector space v is called a banach space if every cauchy sequence in v converges.
Banach space. That is the distance between vectors converges closer to each other as the sequence goes on. A banach space is a complete normed vector space in mathematical analysis. A banach space is a complete vector space with a norm. Two norms and are called equivalent if they give the same topology which is equivalent to the existence of constants and such that.
For all t x t x ˉ d. In the finite dimensional case all norms are equivalent. The hölder spaceck α ˉ d k 0 1 2 0 α 1 is a banach space of functions w w t x that are continuous in ˉ d together with all derivatives of the form drtdsxw t x for 0 2r s k and have the finite norm. 2 hold for all.
In mathematics more specifically in functional analysis a banach space pronounced ˈbanax is a complete normed vector space.
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