Functional analysis: Difference between revisions
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===Closed graph theorem=== | ===Closed graph theorem=== | ||
{{main|Closed graph theorem}} | {{main|Closed graph theorem}} | ||
{{math theorem | name = Closed graph theorem | math_statement = If <math>X</math> is a [[topological space]] and <math>Y</math> is a [[Compact space|compact]] [[Hausdorff space]], then the graph of a linear map <math>T</math> from <math>X</math> to <math>Y</math> is closed if and only if <math>T</math> is [[continuous function (topology)|continuous]].<ref>{{Cite book | last=Munkres | first=James R. | url={{google books |plainurl=y |id=XjoZAQAAIAAJ}} | title=Topology | date=2000 | publisher=Prentice Hall, Incorporated | isbn=978-0-13-181629-9 | language=en | page= 171}}</ref>}} | {{math theorem | name = Closed graph theorem | math_statement = If <math>X</math> is a [[topological vector space]] and <math>Y</math> is a [[Compact space|compact]] [[Hausdorff space|Hausdorff]] topological vector space, then the graph of a linear map <math>T</math> from <math>X</math> to <math>Y</math> is closed if and only if <math>T</math> is [[continuous function (topology)|continuous]].<ref>{{Cite book | last=Munkres | first=James R. |author-link=James Munkres | url={{google books |plainurl=y |id=XjoZAQAAIAAJ}} | title=Topology | date=2000 | publisher=Prentice Hall, Incorporated | isbn=978-0-13-181629-9 | language=en | page= 171}}</ref>}} | ||
===Other topics=== | ===Other topics=== | ||
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* [[Nelson Dunford|Dunford, N.]] and [[Jacob T. Schwartz|Schwartz, J.T.]]: ''Linear Operators, General Theory, John Wiley & Sons'', and other 3 volumes, includes visualization charts | * [[Nelson Dunford|Dunford, N.]] and [[Jacob T. Schwartz|Schwartz, J.T.]]: ''Linear Operators, General Theory, John Wiley & Sons'', and other 3 volumes, includes visualization charts | ||
* Edwards, R. E.: ''Functional Analysis, Theory and Applications'', Hold, Rinehart and Winston, 1965. | * Edwards, R. E.: ''Functional Analysis, Theory and Applications'', Hold, Rinehart and Winston, 1965. | ||
* Eidelman, Yuli, Vitali Milman, and Antonis Tsolomitis: ''Functional Analysis: An Introduction'', American Mathematical Society, 2004. | * Eidelman, Yuli, [[Vitali Milman]], and Antonis Tsolomitis: ''Functional Analysis: An Introduction'', American Mathematical Society, 2004. | ||
* [[Avner Friedman|Friedman, A.]]: ''Foundations of Modern Analysis'', Dover Publications, Paperback Edition, July 21, 2010 | * [[Avner Friedman|Friedman, A.]]: ''Foundations of Modern Analysis'', Dover Publications, Paperback Edition, July 21, 2010 | ||
* Giles, J.R.: ''Introduction to the Analysis of Normed Linear Spaces'', Cambridge University Press, 2000 | * Giles, J.R.: ''Introduction to the Analysis of Normed Linear Spaces'', Cambridge University Press, 2000 | ||