Geodesic
Martingale inequalities and operator space structures on $L_p$
Documenta mathematica, Tome 19 (2014), pp. 1367-1442
Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

We describe a new operator space structure on Lp​ when p is an even integer and compare it with the one introduced in our previous work using complex interpolation. For the new structure, the Khintchine inequalities and Burkholder's martingale inequalities have a very natural form span of the Rademacher functions is completely isomorphic to the operator Hilbert space OH, and the square function of a martingale difference sequence dn​ is Σdn​⊗dˉn​. Various inequalities from harmonic analysis are also considered in the same operator valued framework. Moreover, the new operator space structure also makes sense for non-commutative Lp​-spaces associated to a trace with analogous results. When p→∞ and the trace is normalized, this gives us a tool to study the correspondence E↦E​ defined as follows: if E⊂B(H) is a completely isometric emdedding then E​ is defined so that E​⊂CB(OH) is also one.
DOI : 10.4171/dm/483
Classification : 46B28, 46L53, 47L07, 47L25, 60G48 
@article{10_4171_dm_483,
     author = {Gilles Pisier},
     title = {Martingale inequalities and operator space structures on $L_p$},
     journal = {Documenta mathematica},
     pages = {1367--1442},
     year = {2014},
     volume = {19},
     doi = {10.4171/dm/483},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/483/}
}
TY  - JOUR
AU  - Gilles Pisier
TI  - Martingale inequalities and operator space structures on $L_p$
JO  - Documenta mathematica
PY  - 2014
SP  - 1367
EP  - 1442
VL  - 19
UR  - http://geodesic.mathdoc.fr/articles/10.4171/dm/483/
DO  - 10.4171/dm/483
ID  - 10_4171_dm_483
ER  - 
%0 Journal Article
%A Gilles Pisier
%T Martingale inequalities and operator space structures on $L_p$
%J Documenta mathematica
%D 2014
%P 1367-1442
%V 19
%U http://geodesic.mathdoc.fr/articles/10.4171/dm/483/
%R 10.4171/dm/483
%F 10_4171_dm_483
Gilles Pisier. Martingale inequalities and operator space structures on $L_p$. Documenta mathematica, Tome 19 (2014), pp. 1367-1442. doi: 10.4171/dm/483

Cité par Sources :