翻訳と辞書 Words near each other ・ Douglas XT3D ・ Douglas XTB2D Skypirate ・ Douglas Y. Yongue ・ Douglas Y1B-7 ・ Douglas Yard ・ Douglas Yates ・ Douglas Yeo ・ Douglas YOA-5 ・ Douglas Young ・ Douglas Young (classicist) ・ Douglas Young (cricketer) ・ Douglas Young (judge) ・ Douglas Young (solicitor) ・ Douglas Youvan ・ Douglas Z. Doty ・ Douglas' lemma ・ Douglas' toad ・ Douglas, Alabama ・ Douglas, Arizona ・ Douglas, Augusta and Gulf Railway ・ Douglas, British Columbia ・ Douglas, Canterbury ・ Douglas, Chicago ・ Douglas, County Cork ・ Douglas, Dundee ・ Douglas, Falkland Islands ・ Douglas, Georgia ・ Douglas, Illinois ・ Douglas, Indiana ・ Douglas, Isle of Man 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 Douglas' lemma ： ウィキペディア英語版 Douglas' lemma In operator theory, an area of mathematics, Douglas' lemma relates factorization, range inclusion, and majorization of Hilbert space operators. It is generally attributed to Ronald G. Douglas, although Douglas acknowledges that aspects of the result may already have been known. The statement of the result is as follows: Theorem: If ''A'' and ''B'' are bounded operators on a Hilbert space ''H'', the following are equivalent: # $\backslash text(A)\backslash subseteq\backslash text(B).\backslash ,$ # $AA^$ *\leq\lambda^2 BB^ * for some $\backslash lambda\backslash geq\; 0.\backslash ,$ # There exists a bounded operator ''C'' on ''H'' such that ''A'' = ''BC''. Moreover, if these equivalent conditions hold, then there is a unique operator ''C'' such that * $\backslash Vert\; C\; \backslash Vert^2=\backslash inf\backslash .$ * ker(''A'') = ker(''C'') * $\backslash text(C)\backslash subseteq\backslash overline$ A generalization of Douglas' lemma for unbounded operators on a Banach space is given in. ==See also== Positive operator 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「Douglas' lemma」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.