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| {{Unreferenced|date=December 2009}}
| | The name of the author is definitely Gabrielle Lattimer. For years she's been working whereas a library assistant. For a while she's been in Massachusetts. As a woman what lindsay really likes is mah jongg but she hasn't made a dime with it. She is running and maintaining a blog here: http://circuspartypanama.com<br><br>Feel free to visit my blog post :: [http://circuspartypanama.com clash of clans hack] |
| In [[mathematics]], the '''continuous functional calculus''' of [[operator theory]] and [[C*-algebra]] theory allows applications of continuous functions to normal elements of a C*-algebra. More precisely,
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| '''Theorem'''. Let ''x'' be a [[normal operator|normal]] element of a C*-algebra ''A'' with an identity element e; then there is a unique mapping π : ''f'' → ''f''(''x'') defined for ''f'' a continuous function on the spectrum Sp(''x'') of ''x'' such that π is a unit-preserving morphism of C*-algebras such that π(1) = e and π(ι) = ''x'', where ι denotes the function ''z'' → ''z'' on Sp(''x'').
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| The proof of this fact is almost immediate from the [[Gelfand representation]]: it suffices to assume ''A'' is the C*-algebra of continuous functions on some compact space ''X'' and define
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| :<math> \pi(f) = f \circ x. </math> | |
| Uniqueness follows from application of the [[Stone-Weierstrass theorem]].
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| In particular, this implies that bounded self-adjoint operators on a [[Hilbert space]] have a continuous functional calculus.
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| For the case of self-adjoint [[operator (mathematics)|operator]]s on a Hilbert space of more interest is the [[Borel functional calculus]].
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| {{Functional Analysis}}
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| {{DEFAULTSORT:Continuous Functional Calculus}}
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| [[Category:Functional calculus]]
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| [[Category:Continuous mappings]] | |
| [[Category:C*-algebras]]
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Latest revision as of 18:43, 9 January 2015
The name of the author is definitely Gabrielle Lattimer. For years she's been working whereas a library assistant. For a while she's been in Massachusetts. As a woman what lindsay really likes is mah jongg but she hasn't made a dime with it. She is running and maintaining a blog here: http://circuspartypanama.com
Feel free to visit my blog post :: clash of clans hack