翻訳と辞書 Words near each other ・ Uniformity and jurisdiction in U.S. federal court tax decisions ・ Uniformity of content ・ Uniformity of motive ・ Uniformity policy ・ Uniformity tape ・ Uniformizable space ・ Uniformization ・ Uniformization (probability theory) ・ Uniformization (set theory) ・ Uniformization theorem ・ Uniformly bounded representation ・ Uniformly Cauchy sequence ・ Uniformly connected space ・ Uniformly convex space ・ Uniformly distributed measure ・ Uniformly hyperfinite algebra ・ Uniformly most powerful test ・ Uniformly smooth space ・ Uniformology ・ Uniforms and insignia of the Kriegsmarine ・ Uniforms and insignia of the Schutzstaffel ・ Uniforms and insignia of the Sturmabteilung ・ Uniforms of Iraqi Armed Forces ・ Uniforms of La Grande Armée ・ Uniforms of the American Civil War ・ Uniforms of the Canadian Armed Forces ・ Uniforms of the Confederate States military forces ・ Uniforms of the Imperial Japanese Army ・ Uniforms of the Luftwaffe (1935–1945) ・ Uniforms of the New Zealand Army 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 Uniformly hyperfinite algebra ： ウィキペディア英語版 Uniformly hyperfinite algebra In mathematics, particularly in the theory of C *-algebras, a uniformly hyperfinite, or UHF, algebra is a C *-algebra that can be written as the closure, in the norm topology, of an increasing union of finite-dimensional full matrix algebras. == Definition and classification == A UHF C *-algebra is the direct limit of an inductive system where each ''An'' is a finite-dimensional full matrix algebra and each ''φn'' : ''An'' → ''A''''n''+1 is a unital embedding. Suppressing the connecting maps, one can write :$A\; =\; \backslash overline\; .$ If :$A\_n\; \backslash simeq\; M\_\; (\backslash mathbb\; C),$ then ''r kn'' = ''kn'' + 1 for some integer ''r'' and :$\backslash phi\_n\; (a)\; =\; a\; \backslash otimes\; I\_r,$ where ''Ir'' is the identity in the ''r'' × ''r'' matrices. The sequence ...''kn''|''kn'' + 1|''kn'' + 2... determines a formal product :$\backslash delta(A)\; =\; \backslash prod\_p\; p^$ where each ''p'' is prime and ''tp'' = sup , possibly zero or infinite. The formal product ''δ''(''A'') is said to be the supernatural number corresponding to ''A''. Glimm showed that the supernatural number is a complete invariant of UHF C *-algebras. In particular, there are uncountably many isomorphism classes of UHF C *-algebras. If ''δ''(''A'') is finite, then ''A'' is the full matrix algebra ''M''''δ''(''A''). A UHF algebra is said to be of ''infinite type'' if each ''tp'' in ''δ''(''A'') is 0 or ∞. In the language of K-theory, each supernatural number :$\backslash delta(A)\; =\; \backslash prod\_p\; p^$ specifies an additive subgroup of R that is the rational numbers of the type ''n''/''m'' where ''m'' formally divides ''δ''(''A''). This group is the ''K''0 group of ''A''. 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「Uniformly hyperfinite 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.