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Ideals in $L(L_p)$
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46E30 - Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Kothe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
47B10 - Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.)
47L10 - Algebras of operators on Banach spaces and other topological linear spaces
Additional resources :
https://www.cirm-math.fr/ProgWeebly/Renc1755/Johnson.pdf
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Abstract :
I'll discuss the Banach algebra structure of the spaces of bounded linear operators on $\ell_p$ and $L_p$ := $L_p(0, 1)$. The main new results are
1. The only non trivial closed ideal in $L(L_p)$, 1 $\leq$ p < $\infty$, that has a left approximate identity is the ideal of compact operators (joint with N. C. Phillips and G. Schechtman).
2. There are infinitely many; in fact, a continuum; of closed ideals in $L(L_1)$ (joint with G. Pisier and G. Schechtman).
The second result answers a question from the 1978 book of A. Pietsch, “Operator ideals”.
MSC Codes : 1. The only non trivial closed ideal in $L(L_p)$, 1 $\leq$ p < $\infty$, that has a left approximate identity is the ideal of compact operators (joint with N. C. Phillips and G. Schechtman).
2. There are infinitely many; in fact, a continuum; of closed ideals in $L(L_1)$ (joint with G. Pisier and G. Schechtman).
The second result answers a question from the 1978 book of A. Pietsch, “Operator ideals”.
46E30 - Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Kothe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
47B10 - Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.)
47L10 - Algebras of operators on Banach spaces and other topological linear spaces
Additional resources :
https://www.cirm-math.fr/ProgWeebly/Renc1755/Johnson.pdf
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Information on the Video
Language : EnglishAvailable date : 14/03/2018 Conference Date : 06/03/2018 Subseries : Research talks arXiv category : Functional Analysis Mathematical Area(s) : Analysis and its Applications Format : MP4 (.mp4) - HD Video Time : 00:47:35 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2018-03-06_Johnson.mp4 
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Information on the Event
Event Title : Non linear functional analysis / Analyse fonctionnelle non linéaireDates : 05/03/2018 - 09/03/2018 Event Year : 2018 Event URL : https://conferences.cirm-math.fr/1755.html
Citation Data
DOI : 10.24350/CIRM.V.19371503Cite this video as: (2018). Ideals in $L(L_p)$. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19371503 URI : http://dx.doi.org/10.24350/CIRM.V.19371503 |
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