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en>Yobot: WP:CHECKWIKI error fixes using AWB (10093)

2014-05-05T11:28:42Z

WP:CHECKWIKI error fixes using AWB (10093)

← Older revision		Revision as of 13:28, 5 May 2014
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	~~In the [[mathematics\|mathematical]] theory of [[Banach space]]s~~, the '~~''closed range theorem''' gives necessary and sufficient conditions for a [[closed linear operator\|closed]] [[densely defined operator]] to~~ have ~~[[closed set\|closed]] [[range~~ of a ~~function\|range]]~~. ~~The theorem was proved by [[Stefan Banach]]~~ in ~~his 1932 ''Théorie des opérations linéaires''~~.		They're always ready to help, and they're always making changes to the site to make sure you won't have troubles in the first place. You may discover this probably the most time-consuming part of building a Word - Press MLM website. These templates are professionally designed and are also Adsense ready. Transforming your designs to Word - Press blogs is not that easy because of the simplified way in creating your very own themes. Also our developers are well convergent with the latest technologies and bitty-gritty of wordpress website design and promises to deliver you the best solution that you can ever have. <br><br>Any business enterprise that is certainly worth its name should really shell out a good deal in making sure that they have the most effective website that provides related info to its prospect. You do not catch a user's attention through big and large pictures that usually takes a millennium to load up. If you have any concerns pertaining to wherever and how to use [http://9ja.in/wordpress_backup_plugin_698411 wordpress backup], you can make contact with us at our own webpage. This may possibly also permit it currently being seriously straightforward to modify the hues within your Ad - Sense code so the ads blend nicely with the many term broad internet word wide web web page in case you can come to your conclusion to run the adverts. E-commerce websites are meant to be buzzed with fresh contents, graphical enhancements, and functionalities. By using Word - Press, you can develop very rich, user-friendly and full-functional website. <br><br>The least difficult and very best way to do this is by acquiring a Word - Press site. s cutthroat competition prevailing in the online space won. For a much deeper understanding of simple wordpress themes", check out Upon browsing such, you'll be able to know valuable facts. Thousands of plugins are available in Word - Press plugin's library which makes the task of selecting right set of plugins for your website a very tedious task. " Thus working with a Word - Press powered web application, making any changes in the website design or website content is really easy and self explanatory. <br><br>The next thing I did after installing Wordpress was to find myself a free good-looking Wordpress-theme offering the functionality I was after. php file in the Word - Press root folder and look for this line (line 73 in our example):. Next you'll go by way of to your simple Word - Press site. A whole lot worse, your site will likely be useless as well as your merchandise won't sell if no one has the endurance to wait for the web pages to load. Now all you have to do is log into your Word - Press site making use of the very same username and password that you initially had in your previous site. <br><br>He loves sharing information regarding wordpress, Majento, Drupal and Joomla development tips & tricks. I'm a large fan of using Word - Press to create pretty much any sort of web page. Just download it from the website and start using the same. This is because of the customization that works as a keystone for a SEO friendly blogging portal website. The 2010 voting took place from July 7 through August 31, 2010.

	~~Let~~ <~~math~~>X<~~/math~~> and ~~<math>Y</math> be Banach spaces, <math>T\colon D(T) \~~to Y</~~math> a closed linear operator whose domain <math>D(T)<~~/~~math> is dense~~ in ~~<math>X<~~/~~math>~~, ~~and <math>T'</math>~~ the ~~[[Unbounded_operator#Transpose\|transpose]] of <math>T</math>~~. ~~The theorem asserts that the following conditions~~ are ~~equivalent:~~

	* <math>R(T)</math>, ~~the range of <math>T</math>~~, ~~is closed in <math>Y</math>~~,
	* <math>R(T')</math>, ~~the range of~~ <~~math~~>T'<~~/math~~>, is ~~closed~~ in ~~<math>X'</math>,~~ the ~~[[continuous dual~~ space~~\|dual]]~~ of ~~<math>X</math>~~,
	* <math>R(T) = N(T'~~)^\perp=\{y\~~in Y \| \langle x^,~~y\rangle = 0\quad {\text{for all}}\quad x^\~~in ~~N(T')\}~~<~~/math~~>,
	* <~~math~~>~~R(T') = N(T)^\perp=\{x^\~~in ~~X' \| \langle x^,y\rangle = 0\quad {\text{~~for ~~all}}\quad y\~~in ~~N(T~~)~~\}</math>~~.

	~~Several corollaries are immediate from the theorem~~. ~~For instance~~, ~~a densely defined closed operator <math>T</math>~~ as ~~above~~ has <~~math~~>~~R(T)=Y~~<~~/math~~> if and ~~only if the transpose <math>T~~'~~</math> has~~ a ~~continuous inverse~~. ~~Similarly, <math>R(T') = X'</math> if~~ and ~~only if <math>T</math> has a continuous inverse~~.

	~~== See also ==~~
	* [[Fundamental theorem of ~~linear algebra]]~~

	~~==References==~~
	*{{Citation \| last1=Yosida \| first1=K. ~~\| title=Functional Analysis \| publisher=[[Springer-Verlag]] \| location=Berlin~~, ~~New York \| edition=6th \| series=Grundlehren der Mathematischen Wissenschaften (Fundamental Principles of Mathematical Sciences), vol. 123 \| year=1980}}~~.

	~~{{Functional Analysis}}~~

	~~[[Category:Theorems in functional analysis]]~~

	~~{{mathanalysis-stub}}~~

89.140.161.225: Adding standard denotion of order and size

2012-10-09T11:02:51Z

Adding standard denotion of order and size

← Older revision		Revision as of 13:02, 9 October 2012
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	~~Hello~~. Let ~~me introduce the writer. His name is Major~~ and ~~hubby totally loves this designate. Data processing~~ is ~~where her primary income proceeds from~~ and ~~her salary recently been really fulfilling. New Hampshire has always been her home. To lift weights region I won~~'~~t give move up~~. ~~You can always find her website here: http~~://~~www.vimeo.com~~/~~99423670~~<br><br>~~My page - miley cyrus nude~~, [~~http:~~//~~www~~.~~vimeo~~.~~com~~/~~99423670 vimeo~~.~~com~~],		In the [[mathematics\|mathematical]] theory of [[Banach space]]s, the '''closed range theorem''' gives necessary and sufficient conditions for a [[closed linear operator\|closed]] [[densely defined operator]] to have [[closed set\|closed]] [[range of a function\|range]]. The theorem was proved by [[Stefan Banach]] in his 1932 ''Théorie des opérations linéaires''.

			Let <math>X</math> and <math>Y</math> be Banach spaces, <math>T\colon D(T) \to Y</math> a closed linear operator whose domain <math>D(T)</math> is dense in <math>X</math>, and <math>T'</math> the [[Unbounded_operator#Transpose\|transpose]] of <math>T</math>. The theorem asserts that the following conditions are equivalent:

			* <math>R(T)</math>, the range of <math>T</math>, is closed in <math>Y</math>,
			* <math>R(T')</math>, the range of <math>T'</math>, is closed in <math>X'</math>, the [[continuous dual space\|dual]] of <math>X</math>,
			* <math>R(T) = N(T')^\perp=\{y\in Y \| \langle x^,y\rangle = 0\quad {\text{for all}}\quad x^\in N(T')\}</math>,
			* <math>R(T') = N(T)^\perp=\{x^\in X' \| \langle x^,y\rangle = 0\quad {\text{for all}}\quad y\in N(T)\}</math>.

			Several corollaries are immediate from the theorem. For instance, a densely defined closed operator <math>T</math> as above has <math>R(T)=Y</math> if and only if the transpose <math>T'</math> has a continuous inverse. Similarly, <math>R(T') = X'</math> if and only if <math>T</math> has a continuous inverse.

			== See also ==
			* [[Fundamental theorem of linear algebra]]

			==References==
			*{{Citation \| last1=Yosida \| first1=K. \| title=Functional Analysis \| publisher=[[Springer-Verlag]] \| location=Berlin, New York \| edition=6th \| series=Grundlehren der Mathematischen Wissenschaften (Fundamental Principles of Mathematical Sciences), vol. 123 \| year=1980}}.

			{{Functional Analysis}}

			[[Category:Theorems in functional analysis]]

			{{mathanalysis-stub}}

en>R'n'B: Fix links to disambiguation page Subgraph

2011-11-02T18:11:04Z

Fix links to disambiguation page Subgraph

New page

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