reflexive Banach space

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reflexive Banach space

[ri¦flek·siv ′bä‚näk ‚spās]
(mathematics)
A Banach space B such that, for every continuous linear functional F on the conjugate space B *, there corresponds a point x0 of B such that F (ƒ) = ƒ(x0) for each element ƒ of B *. Also known as regular Banach space.
References in periodicals archive ?
since any compact operator on a reflexive space attains is norm.
Hence Corollary 3 implies Grothendieck's classical result that approximation property implies metric approximation property for separable reflexive spaces.