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Ideals in $L(L_p)$
Multi angle
Authors : Johnson, William B. (Author of the conference)
CIRM (Publisher )
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
CIRM (Publisher )
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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
Film maker : Hennenfent, GuillaumeLanguage : English Available 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 linéaireEvent Organizers : Albiac, Fernando ; Godefroy, Gilles ; Lancien, Gilles Dates : 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: Johnson, William B. (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 |
See Also
- [Post-edited] Coarse dimension reduction / Author of the conference Naor, Assaf.
- [Multi angle] $L^2$ spectral gap and group actions on Banach spaces / Author of the conference de la Salle, Mikael.
- [Multi angle] Finite quotients in coarse geometry / Author of the conference Khukhro, Anastasia.
- [Multi angle] On a difference between two methods of low-distortion embeddings of finite metric spaces into non-superreflexive Banach spaces / Author of the conference Randrianantoanina, Beata.
Bibliography
