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Teorema Lomonosov

 
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Cezar Lupu
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Joined: 26 Sep 2007
Posts: 629
Location: Pittsburgh/Craiova/Bucharest/Constanta

PostPosted: Sun Jun 08, 2008 7:10 pm    Post subject: Teorema Lomonosov Reply with quote

Hai sa incepem aceasta sectiune cu o bomba: Smile

Fie X un spatiu normat si A\in\mathcal{L}_{C}(X) (operator compact), A\neq O_{\mathcal{L}(X)}. Atunci pentru orice B\in\mathcal{L}(X) care nu este scalar si comuta cu A, exista Y\subset{X} propriu, Y inchis, invariant la orice \delta\in\mathcal{L}(X) care comuta cu B.
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Last edited by Cezar Lupu on Sun Jun 08, 2008 7:37 pm; edited 1 time in total
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Mihai Berbec
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Joined: 29 Feb 2008
Posts: 76

PostPosted: Sun Jun 08, 2008 7:34 pm    Post subject: Reply with quote

Teorema spune de fapt ca orice operator care comuta cu un operator compact are subspatii invariante si este adevarata pentru spatii Banach infinit-dimensionale. Demonstratia se gaseste in articolul lui Lomonosov, Invariant subspaces for operators commuting with compact operator, Funkcional Anal. i Priloien, 7:3(1973), pag 55-56 sau in V. Rundle - Linear Analysis si foloseste in mod esential teorema de punct fix a lui Schauder.
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