caa a22 4500 469068558 CHVBK 20180323132915.0 cr unu---uuuuu 170328e19921001xx s 000 0 eng 10.1007/BF02808225 doi (NATIONALLICENCE)springer-10.1007/BF02808225 Lust-Piquard Françoise CNRS-UA D 0757, Université de Paris-Sud Mathématiques, Bât. 425, 91405, Orsay Cedex, France aut A grothendieck factorization theorem on 2-convex schatten spaces [Elektronische Daten] [Françoise Lust-Piquard] We prove that for every bounded linear operatorT:C 2p →H(1≤p<∞,H is a Hilbert space,C 2 p p is the Schatten space) there exists a continuous linear formf onC p such thatf≥0, ‖f‖(C C p)*=1 and $$\forall x \in C^{2p} , \left\| {T(x)} \right\| \leqslant 2\sqrt 2 \left\| T \right\|< f\frac{{x * x + xx*}}{2} > 1/2$$ . Forp=∞ this non-commutative analogue of Grothendieck's theorem was first proved by G. Pisier. In the above statement the Schatten spaceC 2p can be replaced byE E 2 whereE (2) is the 2-convexification of the symmetric sequence spaceE, andf is a continuous linear form onC E. The statement can also be extended toL E{(su2)}(M, τ) whereM is a Von Neumann algebra,τ a trace onM, E a symmetric function space. Hebrew University, 1992 Israel Journal of Mathematics Springer-Verlag 79/2-3(1992-10-01), 331-365 0021-2172 79:2-3<331 1992 79 11856 https://doi.org/10.1007/BF02808225 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02808225 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Lust-Piquard Françoise CNRS-UA D 0757, Université de Paris-Sud Mathématiques, Bât. 425, 91405, Orsay Cedex, France aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer-Verlag 79/2-3(1992-10-01), 331-365 0021-2172 79:2-3<331 1992 79 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer