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{{Distinguish|Gelfond–Schneider theorem}}
== 「それを忘れて、それを忘れて ==


In [[mathematics]], the '''Gelfand–Naimark theorem''' states that an arbitrary [[C*-algebra]] ''A'' is isometrically *-isomorphic to a C*-algebra of [[bounded operator]]s on a [[Hilbert space]]. This result was proven by [[Israel Gelfand]] and [[Mark Naimark]] in 1943 and was a significant point in the development of the theory of C*-algebras since it established the possibility of considering a C*-algebra as an abstract algebraic entity without reference to particular realizations as an [[operator algebra]].
地下悪魔の国、今あなたは私たちが前進遊ぶ与え、私たちは、あなたが自分自身のスクリーンセーバーに頼って生きて身体と息を隠し、前で道をリード！償うことができます。そうでない場合に。後日、容易ではないだろう。 [http://www.aseanacity.com/webalizer/prada-bags-33.html 財布 プラダ レディース] '<br>悪魔の王国は地面に、非常に危険です [http://www.aseanacity.com/webalizer/prada-bags-21.html prada ピンク 財布]。 少し肉は息を示す場合には、多くの未知の悪魔の蛾は、一般的に完全に分割された人々を置くことを急襲します息を隠すように注意し、また、たとえジンDanqiangを<br>。<br>ましてや彼自身のスクリーンセーバーがリリース。<br>それは単に死を求めている [http://www.aseanacity.com/webalizer/prada-bags-30.html プラダ ハンドバッグ]。 今セーバーをリリースし、コールドヘッドの前の広場を作るhuan​​hangrn日シニア姉妹見習いは、全体の安全性が、彼らはより多くの悪魔を破壊することができ、その後、自身が影に隠れて、彼は悪魔を誘致できるようにすることです [http://www.aseanacity.com/webalizer/prada-bags-26.html プラダ 財布 アウトレット]。<br>「それを忘れて、それを忘れて。日シニア姉妹見習いは、ここに第3層の端部である、リスクが莫大である [http://www.aseanacity.com/webalizer/prada-bags-33.html プラダ 財布 メンズ]。あなたは、等
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  <li>[http://107.163.165.17/forum.php?mod=viewthread&tid=481206 http://107.163.165.17/forum.php?mod=viewthread&tid=481206]</li>
 
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The Gelfand–Naimark representation π is the [[direct sum of representations]] π<sub>''f''</sub>
==  パンチの間のこの「ささやかなt 'を ==
of ''A'' where ''f'' ranges over the set of [[pure state]]s of A and π<sub>''f''</sub> is the [[irreducible representation]] associated to ''f'' by the [[GNS construction]].  Thus the Gelfand–Naimark representation acts on
the Hilbert direct sum of the Hilbert spaces ''H''<sub>''f''</sub> by


:<math> \pi(x) [\bigoplus_{f} \xi_f] = \bigoplus_{f} \pi_f(x)\xi_f.</math>
絶対に瞬間、人は知っていた。 パンチの間のこの「ささやかなt プラダ 迷彩 財布 'を<br>、5程度の本体は、実際に完全な5倍の戦闘力で、超暴君無限の強さを果たした プラダ 財布 迷彩。<br>側冷たい目は冷笑、過去に頭部強打、かわすだけでなく、パンチはなかった prada 財布 リボン。 空気中の<br>衝突拳は、「銭tは「驚天動地の悲鳴、目、鼻、厚い肉の弾き出さすべての中で耳を発声し、それが低温側浙江Yiquanが、中に彼の体を入れているようだすべての臓器が打ち砕かれます プラダ 財布 定価。<br>パッと消える！<br>は、血液の雲を放出する、この「ささやかなおじさん「口を見て、その血液が壊れた心臓、肝臓、胆嚢、ならびに肺と混合して、群衆の中で目を驚かせた....​​... 彼が果たしてきた身体へのすべての内臓のパンチの中<br>コールド側が噴出。<br>「殺したくなかったが、私は思わず、アリーナで誰か本当に人の鎖に囲まれています。 プラダ 財布 リボン '牙
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<ul>
 
  <li>?mod=space&uid=35939</li>
 
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</ul>


Note that π(''x'') is a [[bounded linear operator]] since it is the direct sum of a family of operators, each one having norm ≤ ||''x''||.
== altar posted the tyranny of the seal ==


'''Theorem'''. The Gelfand–Naimark representation of a C*-algebra is an isometric *-representation.
Depths of heaven, did not know came to the cold [http://www.aseanacity.com/webalizer/prada-bags-24.html prada ベルト] side of that weight, but do not know what the temple, anyway, he is the seventh temple from the depths, felt a breath of tyranny everywhere, and immediately found a seat [http://www.aseanacity.com/webalizer/prada-bags-31.html プラダ 財布 新作 2014] on the altar, altar posted the tyranny of the seal, the [http://www.aseanacity.com/webalizer/prada-bags-27.html プラダ 財布 スタッズ] seal inside the magic gas [http://www.aseanacity.com/webalizer/prada-bags-28.html prada ピンク 財布] soaring, the above is written in a Heaven's Soldiers letters of the word.<br>'seal of the land?'<br>looked at the rows of cold side altar, seal, saw a huge plaque, written in text above four Once upon a time, next to a stone, stone written with the seal of the land above the origins, about heaven [http://www.aseanacity.com/webalizer/prada-bags-30.html プラダ 財布] in Chronicles crusade in the process, arresting some difficult to eliminate, or valuable devil will seal in this altar among Zuozuo.<br>palm shoot, Fang Han Jun Talisman directly charged that day, and immediately rushed to the altar of a boundless black gas up immediately, a statue of ancient devil, slowly appeared world with life's breath, shook the spot, which first
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</ul>


It suffices to show the map π is [[injective]], since for *-morphisms of C*-algebras injective implies isometric. Let ''x'' be a non-zero element of ''A''.  By the [[Krein extension theorem]] for positive [[linear functional]]s, there is a state ''f'' on ''A'' such that ''f''(''z'') ≥ 0 for all non-negative z in ''A'' and ''f''(&minus;''x''* ''x'') < 0.  Consider the GNS representation π<sub>''f''</sub> with [[cyclic vector]] ξ. Since
== a claw broken coke fly's body ==


:<math> \|\pi_f(x) \xi\|^2 = \langle \pi_f(x) \xi \mid \pi_f(x) \xi \rangle = \langle \xi \mid \pi_f(x^*) \pi_f(x) \xi \rangle = \langle \xi \mid \pi_f(x^* x) \xi \rangle= f(x^* x) > 0, </math>
Injuries.<br>Kacha, coke fly's body to [http://www.aseanacity.com/webalizer/prada-bags-25.html プラダの財布] resist a bit, but it is of no use, directly beaten begins split, Flesh. Lian Jian Qi whole body are broken out.<br>'Is is fake? there is no reason so fragile, Shajie Dao sword is in the product, the power [http://www.aseanacity.com/webalizer/prada-bags-29.html 財布 ブランド プラダ] of infinity, even if I use their lives map, eight Buddha Quanliyiji, they can not kill it at the coke fly only One possibility, that he is in great curse magic sword [http://www.aseanacity.com/webalizer/prada-bags-27.html プラダ 財布 値段] intention to deceive me. '<br>a claw broken coke fly's body, [http://www.aseanacity.com/webalizer/prada-bags-31.html プラダ 長財布] did not gain anything cold side.<br>saver but is deep in your own kernel, sudden movement, strength, Wind \u0026 [http://www.aseanacity.com/webalizer/prada-bags-34.html プラダ 財布 リボン] Fire amulet actually look ten times worse! Great desire surgery seal, even had a vague loose. Not the focus seemed to be just killed avatar fly, but the cold side of himself.<br>'cold side, you just kill, not me, but your own! I just that sword, beheaded in your
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</ul>


it follows that π<sub>''f''</sub> ≠ 0. Injectivity of π follows.
== force shrouded down ==


The construction of Gelfand–Naimark ''representation'' depends only on the GNS construction and therefore it is meaningful for any [[Banach *-algebra]] ''A'' having an [[approximate identity]]. In general it will not be a [[faithful representation]].  The closure of the image of π(''A'')  will be a C*-algebra of operators called the [[C*-enveloping algebra]] of ''A''. Equivalently, we can define the
Above, the grand and broad, seems to be the secular world, are turning to majestic pagoda.<br>mantra resounded through the void, force shrouded down, even thorough the vast Makino all flesh are sealed in them.<br>Makino vast desperately running.<br>'ruling seven-in the last one style .........'<br>He tried to cast out the last great Shazhao, breath into the sky, the sky changes from happening again, the sky a Road shocking rift seems to have had a rift Heaven.<br>have a strong presence, issued an angry growl in [http://www.aseanacity.com/webalizer/prada-bags-31.html プラダ 財布 中古] heaven.<br>Once upon a crystal wall leading to the secular system seems [http://www.aseanacity.com/webalizer/prada-bags-29.html 財布 ブランド プラダ] to [http://www.aseanacity.com/webalizer/prada-bags-31.html プラダ 財布 リボン] be torn, [http://www.aseanacity.com/webalizer/prada-bags-29.html 財布 ブランド プラダ] really strong presence of heaven heavens ignoring the law coming down.<br>everyone jumpy.<br>'I do not know Makino vast ruling last seven [http://www.aseanacity.com/webalizer/prada-bags-25.html プラダ人気財布] type can not be cast get out.'<br>'certainly was cast out of heaven and earth have had
C*-enveloping algebra as follows: Define a real valued function on ''A'' by
相关的主题文章：
:<math> \|x\|_{\operatorname{C}^*} = \sup_f \sqrt{f(x^* x)} </math>
<ul>
as ''f'' ranges over pure states of ''A''.   This is a semi-norm, which we refer to as the ''C* semi-norm'' of ''A''. The set '''I''' of elements of ''A'' whose semi-norm is 0 forms a two sided-ideal in ''A'' closed under involution. Thus the [[quotient space (linear algebra)|quotient vector space]] ''A'' / '''I''' is an involutive algebra and the norm
 
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  </ul>


:<math> \| \cdot \|_{\operatorname{C}^*} </math>
== 'God seed ==


[[factorization|factor]]s through a norm on ''A'' / '''I''', which except for completeness, is a C* norm on  ''A'' / '''I''' (these are sometimes called pre-C*-norms). Taking the completion of ''A'' / '''I''' relative to this pre-C*-norm produces a C*-algebra ''B''.
Inter, though God really is the king of the seven Abi magic gas billowing wrap, but SG flashing around the body, not afraid to be refining.<br>their lives [http://www.aseanacity.com/webalizer/prada-bags-33.html プラダ メンズ ベルト] even though [http://www.aseanacity.com/webalizer/prada-bags-35.html プラダ スタッズ 財布] they could not figure out the scope, but it can not hurt people.<br>'God seed!'<br>side cold look, [http://www.aseanacity.com/webalizer/prada-bags-29.html 財布 ブランド プラダ] and sure enough it saw some clues in the seven Gods inside the body, it seems that there is a seed. Once, when his injury will not stop rotating, tied emptiness learned from a strange force, repair the body. Even their lives map, they can not prevent infiltration of this force.<br>now somewhat similar to the seven gods trapped in UDL cold side among the immortals. Fang Han had with the 'World Tree' draws upon a [http://www.aseanacity.com/webalizer/prada-bags-23.html prada スタッズ 財布] strength, and now [http://www.aseanacity.com/webalizer/prada-bags-23.html prada スタッズ 財布] the seven gods with God seed, learn what 'imaginary spirit world' power. So I can not kill them.<br>Obviously, 'imaginary spirit world' is the Protoss place to live, though
 
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By the [[Krein–Milman theorem]] one can show without too much difficulty that for ''x'' an element of the [[Banach *-algebra]] ''A'' having an approximate identity:
<ul>
:<math> \sup_{f \in \operatorname{State}(A)} f(x^*x) = \sup_{f \in \operatorname{PureState}(A)} f(x^*x). </math>
 
It follows that an equivalent form for the C* norm on ''A'' is to take the above supremum over all states.
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The universal construction is also used to define [[universal C*-algebra]]s of isometries.
  <li>[http://www.351360.com/bbs/forum.php?mod=viewthread&tid=62790 http://www.351360.com/bbs/forum.php?mod=viewthread&tid=62790]</li>
 
 
'''Remark'''. The [[Gelfand representation]] or  [[Gelfand isomorphism]] for a commutative C*-algebra with unit <math>A</math> is an isometric *-isomorphism from <math>A</math> to the algebra of continuous complex-valued functions on the space of multiplicative linear functionals, which in the commutative case are precisely the pure states, of ''A'' with the weak* topology.
  <li>[http://fmgradio.com/mt/mt-search.cgi http://fmgradio.com/mt/mt-search.cgi]</li>
 
 
==References==
</ul>
* {{cite journal |author=[[I. M. Gelfand]], [[M. A. Naimark]] |title=On the imbedding of normed rings into the ring of operators on a Hilbert space |journal=Math. Sbornik |volume=12 |issue=2 |year=1943 |pages=197–217 |url=http://mi.mathnet.ru/eng/msb6155}} (also [http://www.google.com/books?id=DYCUp0JYU6sC&printsec=frontcover#PPA3,M1 available from Google Books])
 
* {{citation|first=Jacques|last=Dixmier|authorlink=Jacques Dixmier|title=Les C*-algèbres et leurs représentations|publisher=Gauthier-Villars|year=1969|isbn=0-7204-0762-1}}, also available in English from North Holland press, see in particular sections 2.6 and 2.7.
 
{{DEFAULTSORT:Gelfand-Naimark theorem}}
[[Category:Functional analysis]]
[[Category:Operator theory]]
[[Category:Theorems in functional analysis]]

Latest revision as of 10:38, 13 January 2015

「それを忘れて、それを忘れて

地下悪魔の国、今あなたは私たちが前進遊ぶ与え、私たちは、あなたが自分自身のスクリーンセーバーに頼って生きて身体と息を隠し、前で道をリード！償うことができます。そうでない場合に。後日、容易ではないだろう。 財布 プラダ レディース '
悪魔の王国は地面に、非常に危険です prada ピンク 財布。 少し肉は息を示す場合には、多くの未知の悪魔の蛾は、一般的に完全に分割された人々を置くことを急襲します息を隠すように注意し、また、たとえジンDanqiangを
。
ましてや彼自身のスクリーンセーバーがリリース。
それは単に死を求めている プラダ ハンドバッグ。 今セーバーをリリースし、コールドヘッドの前の広場を作るhuan​​hangrn日シニア姉妹見習いは、全体の安全性が、彼らはより多くの悪魔を破壊することができ、その後、自身が影に隠れて、彼は悪魔を誘致できるようにすることです プラダ 財布 アウトレット。
「それを忘れて、それを忘れて。日シニア姉妹見習いは、ここに第3層の端部である、リスクが莫大である プラダ 財布 メンズ。あなたは、等 相关的主题文章：

 パンチの間のこの「ささやかなt 'を

絶対に瞬間、人は知っていた。 パンチの間のこの「ささやかなt プラダ 迷彩 財布 'を
、5程度の本体は、実際に完全な5倍の戦闘力で、超暴君無限の強さを果たした プラダ 財布 迷彩。
側冷たい目は冷笑、過去に頭部強打、かわすだけでなく、パンチはなかった prada 財布 リボン。 空気中の
衝突拳は、「銭tは「驚天動地の悲鳴、目、鼻、厚い肉の弾き出さすべての中で耳を発声し、それが低温側浙江Yiquanが、中に彼の体を入れているようだすべての臓器が打ち砕かれます プラダ 財布 定価。
パッと消える！
は、血液の雲を放出する、この「ささやかなおじさん「口を見て、その血液が壊れた心臓、肝臓、胆嚢、ならびに肺と混合して、群衆の中で目を驚かせた....​​... 彼が果たしてきた身体へのすべての内臓のパンチの中
コールド側が噴出。
「殺したくなかったが、私は思わず、アリーナで誰か本当に人の鎖に囲まれています。 プラダ 財布 リボン '牙 相关的主题文章：

  • ?mod=space&uid=35939
  • ?mod=viewthread&tid=31349&fromuid=10016

altar posted the tyranny of the seal

Depths of heaven, did not know came to the cold prada ベルト side of that weight, but do not know what the temple, anyway, he is the seventh temple from the depths, felt a breath of tyranny everywhere, and immediately found a seat プラダ 財布 新作 2014 on the altar, altar posted the tyranny of the seal, the プラダ 財布 スタッズ seal inside the magic gas prada ピンク 財布 soaring, the above is written in a Heaven's Soldiers letters of the word.
'seal of the land?'
looked at the rows of cold side altar, seal, saw a huge plaque, written in text above four Once upon a time, next to a stone, stone written with the seal of the land above the origins, about heaven プラダ 財布 in Chronicles crusade in the process, arresting some difficult to eliminate, or valuable devil will seal in this altar among Zuozuo.
palm shoot, Fang Han Jun Talisman directly charged that day, and immediately rushed to the altar of a boundless black gas up immediately, a statue of ancient devil, slowly appeared world with life's breath, shook the spot, which first 相关的主题文章：

a claw broken coke fly's body

Injuries.
Kacha, coke fly's body to プラダの財布 resist a bit, but it is of no use, directly beaten begins split, Flesh. Lian Jian Qi whole body are broken out.
'Is is fake? there is no reason so fragile, Shajie Dao sword is in the product, the power 財布 ブランド プラダ of infinity, even if I use their lives map, eight Buddha Quanliyiji, they can not kill it at the coke fly only One possibility, that he is in great curse magic sword プラダ 財布 値段 intention to deceive me. '
a claw broken coke fly's body, プラダ 長財布 did not gain anything cold side.
saver but is deep in your own kernel, sudden movement, strength, Wind \u0026 プラダ 財布 リボン Fire amulet actually look ten times worse! Great desire surgery seal, even had a vague loose. Not the focus seemed to be just killed avatar fly, but the cold side of himself.
'cold side, you just kill, not me, but your own! I just that sword, beheaded in your 相关的主题文章：

force shrouded down

Above, the grand and broad, seems to be the secular world, are turning to majestic pagoda.
mantra resounded through the void, force shrouded down, even thorough the vast Makino all flesh are sealed in them.
Makino vast desperately running.
'ruling seven-in the last one style .........'
He tried to cast out the last great Shazhao, breath into the sky, the sky changes from happening again, the sky a Road shocking rift seems to have had a rift Heaven.
have a strong presence, issued an angry growl in プラダ 財布 中古 heaven.
Once upon a crystal wall leading to the secular system seems 財布 ブランド プラダ to プラダ 財布 リボン be torn, 財布 ブランド プラダ really strong presence of heaven heavens ignoring the law coming down.
everyone jumpy.
'I do not know Makino vast ruling last seven プラダ人気財布 type can not be cast get out.'
'certainly was cast out of heaven and earth have had 相关的主题文章：

'God seed

Inter, though God really is the king of the seven Abi magic gas billowing wrap, but SG flashing around the body, not afraid to be refining.
their lives プラダ メンズ ベルト even though プラダ スタッズ 財布 they could not figure out the scope, but it can not hurt people.
'God seed!'
side cold look, 財布 ブランド プラダ and sure enough it saw some clues in the seven Gods inside the body, it seems that there is a seed. Once, when his injury will not stop rotating, tied emptiness learned from a strange force, repair the body. Even their lives map, they can not prevent infiltration of this force.
now somewhat similar to the seven gods trapped in UDL cold side among the immortals. Fang Han had with the 'World Tree' draws upon a prada スタッズ 財布 strength, and now prada スタッズ 財布 the seven gods with God seed, learn what 'imaginary spirit world' power. So I can not kill them.
Obviously, 'imaginary spirit world' is the Protoss place to live, though 相关的主题文章：

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