A necessary and sufficient condition for an operator space to support a multiplication making it completely isometric and isomorphic to a unital operator algebra is proved. The condition involves only the holomorphic structure of the Banach spaces underlying the operator space.

In 1965, Ron Douglas proved that if X is a closed subspace of an L1-space and X is isometric to another L1-space, then X is the range of a contractive projection on the containing L1-space. In 1977 Arazy-Friedman showed that if a subspace X of C1 is isometric to another C1-space (possibly finite dimensional), then there is a contractive projection of C1 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. © 2011 Hebrew University Magnes Press.

We define a family of Hilbertian operator spaces Hkn, 1 ≤ k ≤ n, containing the row and column Hilbert spaces Rn, Cn and show that an atomic subspace X ⊂ B(H) which is the range of a contractive projection on B(H) is isometrically completely contractive to an ℓ∞-sum of the Hkn and Cartan factors of types 1 to 4. We also give a classification up to complete isometry of w*-closed atomic JW*-triples which have no infinite-dimensional rank 1 w*-closed ideal. © 2000 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS.

We prove that an operator space is completely isometric to a ternary ring of operators if and only if the open unit balls of all of its matrix spaces are bounded symmetric domains. From this we obtain an operator space characterization of C*-algebras.

Parallel to the study of finite-dimensional Banach spaces, there is a growing interest in the corresponding local theory of operator spaces. We define a family of Hilbertian operator spaces Hnk, 1 ≤ k ≤ n, generalizing the row and column Hilbert spaces Rn and Cn, and we show that an atomic subspace X ⊂ B(H) that is the range of a contractive projection on B(H) is isometrically completely contractive to an l∞-sum of the Hnk and Cartan factors of types 1 to 4. In particular, for finite-dimensional X, this answers a question posed by Oikhberg and Rosenthal. Explicit in the proof is a classification up to complete isometry of atomic w*-closed JW*-triples without an infinite-dimensional rank 1 w*-closed ideal.

The operator spaces H nk, 1 ≤ k ≤ n, generalizing the row and column Hilbert spaces, and arising in the authors' previous study of contractively complemented subspaces of C*-algebras, are shown to be homogeneous and completely isometric to a space of creation operators on a subspace of the anti-symmetric Fock space. The completely bounded Banach-Mazur distance from H nk to a row or column space is explicitly calculated. ©2005 American Mathematical Society.

An atomic decomposition is proved for Danach spaces which satisfy some affine geometric axioms compatible with notions from the quantum mechanical measuring process. This is then applied to yield, under appropriate assumptions, geometric characterizations, up to isometry, of the unit ball of the dual space of a J B*-triple, and up to complete isometry, of one-sided ideals in C*-algebras.

We construct some separable infinite-dimensional homogeneous Hilbertian operator spaces H∞m, R and H∞m, L, which generalize the row and column spaces R and C (the case m = 0). We show that a separable infinite-dimensional Hilbertian JC*-triple is completely isometric to one of H∞m, R, H∞m, L, H∞m, R ∩ H∞m, L, or the space Φ spanned by creation operators on the full anti-symmetric Fock space. In fact, we show that H∞m, L (respectively H∞m, R) is completely isometric to the space of creation (respectively annihilation) operators on the m (respectively m + 1) anti-symmetric tensors of the Hilbert space. Together with the finite-dimensional case studied in [M. Neal, B. Russo, Representation of contractively complemented Hilbertian operator spaces on the Fock space, Proc. Amer. Math. Soc. 134 (2006) 475-485], this gives a full operator space classification of all rank-one JC*-triples in terms of creation and annihilation operator spaces. We use the above structural result for Hilbertian JC*-triples to show that all contractive projections on a C*-algebra A with infinite-dimensional Hilbertian range are "expansions" (which we define precisely) of normal contractive projections from A* * onto a Hilbertian space which is completely isometric to R, C, R ∩ C, or Φ. This generalizes the well-known result, first proved for B ( H ) by Robertson in [A.G. Robertson, Injective matricial Hilbert spaces, Math. Proc. Cambridge Philos. Soc. 110 (1991) 183-190], that all Hilbertian operator spaces that are completely contractively complemented in a C*-algebra are completely isometric to R or C. We use the above representation on the Fock space to compute various completely bounded Banach-Mazur distances between these spaces, or Φ. © 2006 Elsevier Inc. All rights reserved.

Platelets are damage sentinels of the intravascular compartment, initiating and coordinating the primary response to tissue injury. Severe trauma and hemorrhage induce profound alterations in platelet behavior. During the acute post-injury phase, platelets develop a state of impaired ex vivo agonist responsiveness independent of platelet count, associated with systemic coagulopathy and mortality risk. In patients surviving the initial insult, platelets become hyper-responsive, associated with increased risk of thrombotic events. Beyond coagulation, platelets constitute part of a sterile inflammatory response to injury: both directly through release of immunomodulatory molecules, and indirectly through modifying behavior of innate leukocytes. Both procoagulant and proinflammatory aspects have implications for secondary organ injury and multiple-organ dysfunction syndromes. This review details our current understanding of adaptive and maladaptive alterations in platelet biology induced by severe trauma, mechanisms underlying these alterations, potential platelet-focused therapies, and existing knowledge gaps and their research implications.

The endothelial exocytosis of high-molecular-weight multimeric von Willebrand factor (vWF) may occur in critical illness states, including trauma and sepsis, leading to the sustained elevation and altered composition of plasma vWF. These critical illnesses involve the common process of sympathoadrenal activation and loss of the endothelial glycocalyx. As a prothrombotic and proinflammatory molecule that interacts with the endothelium, the alterations exhibited by vWF in critical illness have been implicated in the development and damaging effects of downstream pathologies, such as disseminated intravascular coagulation and systemic inflammatory response syndrome. Given the role of vWF in these pathologies, there has been a recent push to further understand how the molecule may be involved in the pathophysiology of related diseases, such as trauma-induced coagulopathy and acute renal injury, which are also known to develop secondarily to critical illness states. Elucidation of the role of vWF across the broader spectrum of generalized pathologies may provide a basis for the development of novel preventative and restorative measures, while also bolstering the scaffold of more widely used treatments, such as the administration of plasma-containing blood products.