Completely 1-complemented subspaces of Schatten spaces

Merdy, Christian Le; Ricard, Éric; Roydor, Jean

doi:10.1090/s0002-9947-08-04594-7

Cited by 9 publications

(4 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Operator space structure of JC * -triples of this kind has been investigated in the important series of articles [21,20,22] in the case when E is reflexive, equivalently, when E is a finite ℓ ∞ -sum of reflexive Cartan factors. Cartan factors also figure prominently in the study of completely contractively complemented subspaces of Schatten spaces [18].…”

Section: Introductionmentioning

confidence: 99%

Operator space structure of JC*-triples and TROs, I

2011

View full text Add to dashboard Cite

We embark upon a systematic investigation of operator space structure of J C * -triples via a study of the TROs (ternary rings of operators) they generate. Our approach is to introduce and develop a variety of universal objects, including universal TROs, by which means we are able to describe all possible operator space structures of a J C * -triple. Via the concept of reversibility we obtain characterisations of universal TROs over a wide range of examples. We apply our results to obtain explicit descriptions of operator space structures of Cartan factors regardless of dimension Keywords CAR algebra · Cartan factor · JC-operator space · Operator space ideal · Reversibility · Ternary ring of operators · Universal TRO Mathematics Subject Classification (2000) 47L25 · 17C65 · 46L70

show abstract

Section: Introductionmentioning

confidence: 99%

Operator space structure of JC*-triples and TROs, I

2011

View full text Add to dashboard Cite

show abstract

“…A sub-category S of B is projectively rigid if it has the property that whenever A is an object of S and X is a subspace of A which is isometric to an object in S, then X is the range of a morphism of S on A which is a projection. Examples of projectively rigid categories are fewer in number (all are projectively stable), namely, (1) p , 1 < p < ∞, contractions (Pelczynski 1960 [33]), (2) L p , 1 ≤ p < ∞, contractions (Douglas 1965 [10], Ando 1966 [2], Bernau-Lacey 1974 [7]), (3) C p , 1 ≤ p < ∞, contractions (Arazy-Friedman 1977 [3]), (4) Preduals of von Neumann algebras, contractions (Kirchberg 1993 [28]), (5) Preduals of T ROs, complete contractions (Ng-Ozawa 2002 [32]), (6) C p , 1 ≤ p < ∞, p = 2; complete contractions (LeMerdy, Ricard, Roydor 2009 [29]). …”

Section: Introductionmentioning

confidence: 99%

Existence of contractive projections on preduals of JBW*-triples

Neal

Russo

2011

Isr. J. Math.

View full text Add to dashboard Cite

In 1965, Ron Douglas proved that if X is a closed subspace of an L 1 -space and X is isometric to another L 1 -space, then X is the range of a contractive projection on the containing L 1 -space. In 1977 Arazy-Friedman showed that if a subspace X of C 1 is isometric to another C 1 -space (possibly finite dimensional), then there is a contractive projection of C 1 onto X. In 1993 Kirchberg proved that if a subspace X of the predual of a von Neumann algebra M is isometric to the predual of another von Neumann algebra, then there is a contractive projection of the predual of M onto X.We widen significantly the scope of these results by showing that if a subspace X of the predual of a JBW * -triple A is isometric to the predual of another JBW * -triple B, then there is a contractive projection on the predual of A with range X, as long as B does not have a direct summand which is isometric to a space of the form L ∞ (Ω, H), where H is a Hilbert space of dimension at least two. The result is false without this restriction on B.

show abstract

“…Introduction. The results of this paper are taken from [8]. The study of subspaces of L p (1 ≤ p = 2 < ∞) which are the range of a contractive projection (1-complemented subspaces in short) begun in the sixties.…”

mentioning

confidence: 99%

“…Our purpose is to describe the completely 1-complemented subspaces of S p (H). Here we will suppose H separable but the main results are valid for H non-separable (see [8]). …”

mentioning

confidence: 99%