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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Fredholm kernel ： ウィキペディア英語版 Fredholm kernel In mathematics, a Fredholm kernel is a certain type of a kernel on a Banach space, associated with nuclear operators on the Banach space. They are an abstraction of the idea of the Fredholm integral equation and the Fredholm operator, and are one of the objects of study in Fredholm theory. Fredholm kernels are named in honour of Erik Ivar Fredholm. Much of the abstract theory of Fredholm kernels was developed by Alexander Grothendieck and published in 1955. ==Definition== Let ''B'' be an arbitrary Banach space, and let ''B'' * be its dual, that is, the space of bounded linear functionals on ''B''. The tensor product $B^$ *\otimes B has a completion under the norm :$\backslash Vert\; X\; \backslash Vert\_\backslash pi\; =$ \inf \sum_} e^ *_i \otimes e_i \in B^ *\otimes B The completion, under this norm, is often denoted as :$B^$ * \widehat_\pi B and is called the projective topological tensor product. The elements of this space are called Fredholm kernels. 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「Fredholm kernel」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.