|
In mathematics, in the theory of Banach spaces, Dvoretzky's theorem is an important structural theorem proved by Aryeh Dvoretzky in the early 1960s. It answered a question of Alexander Grothendieck. A new proof found by Vitali Milman in the 1970s was one of the starting points for the development of asymptotic geometric analysis (also called ''asymptotic functional analysis'' or the ''local theory of Banach spaces''). ==Original formulation== For every natural number ''k'' ∈ N and every ''ε'' > 0 there exists ''N''(''k'', ''ε'') ∈ N such that if (''X'', ‖.‖) is a Banach space of dimension ''N''(''k'', ''ε''), there exist a subspace ''E'' ⊂ ''X'' of dimension ''k'' and a positive quadratic form ''Q'' on ''E'' such that the corresponding Euclidean norm : on ''E'' satisfies: : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Dvoretzky's theorem」の詳細全文を読む スポンサード リンク
|