Banach Space
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.
Banach space. 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.
That is the distance between vectors converges closer to each other as the sequence goes on. In the finite dimensional case all norms are equivalent. In mathematics more specifically in functional analysis a banach space pronounced ˈbanax is a complete normed vector space.
A banach space is a complete normed vector space in mathematical analysis. W k α sup p d 0 2r s k drtdsxw p sup p p. 2 hold for all.