翻訳と辞書 Words near each other ・ Nessus (mythology) ・ Nessus (Pierson's Puppeteer) ・ Nessus (software) ・ NESSUS Probabilistic Analysis Software ・ Nessy Learning Programme ・ Nessy Tales ・ NEST ・ Nest ・ Nest (album) ・ Nest (band) ・ Nest (disambiguation) ・ Nest (magazine) ・ Nest (protein structural motif) ・ NEST (software) ・ Nest (The Outer Limits) ・ Nest algebra ・ Nest bloet ・ Nest box ・ Nest box camera ・ Nest Family Entertainment ・ Nest ferch Cadell ・ Nest ferch Rhys ・ NEST Foundation ・ Nest Island ・ Nest Labs ・ Nest Lake ・ Nest of Angels ・ Nest Seekers International ・ NEST+m ・ Nest-building in primates Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Nest algebra ： ウィキペディア英語版 Nest algebra In functional analysis, a branch of mathematics, nest algebras are a class of operator algebras that generalise the upper-triangular matrix algebras to a Hilbert space context. They were introduced by and have many interesting properties. They are non-selfadjoint algebras, are closed in the weak operator topology and are reflexive. Nest algebras are among the simplest examples of commutative subspace lattice algebras. Indeed, they are formally defined as the algebra of bounded operators leaving invariant each subspace contained in a subspace nest, that is, a set of subspaces which is totally ordered by inclusion and is also a complete lattice. Since the orthogonal projections corresponding to the subspaces in a nest commute, nests are commutative subspace lattices. By way of an example, let us apply this definition to recover the finite-dimensional upper-triangular matrices. Let us work in the $n$-dimensional complex vector space $\backslash mathbb^n$, and let $e\_1,e\_2,\backslash dots,e\_n$ be the standard basis. For $j=0,1,2,\backslash dots,n$, let $S\_j$ be the $j$-dimensional subspace of $\backslash mathbb^n$ spanned by the first $j$ basis vectors $e\_1,\backslash dots,e\_j$. Let :$N=\backslash ^n\; \backslash \};$ then ''N'' is a subspace nest, and the corresponding nest algebra of ''n'' × ''n'' complex matrices ''M'' leaving each subspace in ''N'' invariant   that is, satisfying $MS\backslash subseteq\; S$ for each ''S'' in ''N'' – is precisely the set of upper-triangular matrices. If we omit one or more of the subspaces ''Sj'' from ''N'' then the corresponding nest algebra consists of block upper-triangular matrices. ==Properties== * Nest algebras are hyperreflexive with distance constant 1. 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「Nest algebra」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.