On the facial structure of the unit balls in a GL-space and its dual

In the early sixties Effros[9] and Prosser[14] studied, in independent work, the duality of the faces of the positive cones in a von Neumann algebra and its predual space. In an implicit way, this work was generalized to certain ordered Banach spaces in papers of Alfsen and Shultz [3] in the seventies, the duality being given in terms of faces of the base of the cone in a base norm space and the faces of the positive cone of the dual space. The present paper is concerned with the facial structure of the unit balls in an ordered Banach space and its dual as well as the duality that reigns between these structures. Specifically, the main results concern the sets of norm-exposed and norm-semi-exposed faces of the unit ball V1 in a GL-space or complete base norm space V and the sets of weak*-exposed and weak*-semi-exposed faces of the unit ball in its dual space V* which forms a unital GM-space or a complete order unit spac

Smoothness Properties of the Unit Ball in a JB*-Triple

An element a of norm one in a JB*-triple A is said to be smooth if there exists a unique element x in the unit ball A1* of the dual A* of A at which a attains its norm, and is said to be Fréchet-smooth if, in addition, any sequence (xn) of elements in A1* for which (xn(a)) converges to one necessarily converges in norm to x. The sequence (a2n+1) of odd powers of a converges in the weak*-topology to a tripotent u(a) in the JBW*-envelope A** of A. It is shown that a is smooth if and only if u(a) is a minimal tripotent in A** and a is Fréchet-smooth if and only if, in addition, u(a) lies in

On the Facial Structure of the Unit Balls in a JBW*-Triple and its Predual

The set of tripotents in a JBW*-triple U with its natural ordering and with a largest element adjoined is shown to be a complete lattice, order isomorphic to the lattice of norm closed faces in the unit ballU*1 of the predual U* of U and anti-order isomorphic to the lattice of weak* closed faces of the unit ball U1 in U. As a consequence, the set of partial isometries in a W*-algebra with its natural ordering and again with a largest element adjoined forms a complete lattice and every non-empty weak* closed face of its unit ball is of the form u+(1−uu*)U (1−u*u)1for some unique partial isometry

Structural Projections on JBW*-Triples

A linear projection R on a Jordan*-triple A is said to be structural provided that, for all elements a, b and c in A, the equality {Rab Rc} = R{a Rbc} holds. A subtriple B of A is said to be complemented if A = B + Ker(B), where Ker(B) = {a∈A: {B a B} = 0}. It is shown that a subtriple of a JBW*-triple is complemented if and only if it is the range of a structural projection. A weak* closed subspace B of the dual E* of a Banach space E is said to be an N*-ideal if every weak* continuous linear functional on B has a norm preserving extension to a weak* continuous linear functional on E* and the set of elements in E which attain their norm on the unit ball in B is a subspace of E. It is shown that a subtriple of a JBW*-triple A is complemented if and only if it is an N*-ideal, from which it follows that complemented subtriples of A are weak* closed, and structural projections on A are weak* continuous and norm non-increasing. It is also shown that every N*-ideal in A possesses a triple product with respect to which it is a JBW*-triple which is isomorphic to a complemented subtriple of

Compact tripotents in bi-dual JB*-triples

The set consisting of the partially ordered set of tripotents in a JBW*-triple C with a greatest element adjoined forms a complete lattice. This paper is mainly concerned with the situation in which C is the second dual A** of a complex Banach space A and, more particularly, when A is itself a JB*-triple. A subset of consisting of the set of tripotents compact relative to A (denned in Section 4) with a greatest element adjoined is studied. It is shown to be an atomic complete lattice with the properties that the infimum of an arbitrary family of elements of is the same whether taken in or in and that every decreasing net of non-zero elements of has a non-zero infimum. The relationship between the complete lattice and the complete lattice where B is a Banach space such that B** is a weak*-closed subtriple of A** is also investigated. When applied to the special case in which A is a C*-algebra the results provide information about the set of compact partial isometries relative to A and are closely related to those recently obtained by Akemann and Pedersen. In particular it is shown that a partial isometry is compact relative to A if and only if, in their terminology, it belongs locally to A. The main results are applied to this and other example

Long-Term Antibiotic Cost Savings from a Comprehensive Intervention Program in a Medical Department of a University-Affiliated Teaching Hospital

We tested a low-cost, multifaceted intervention program comprising formulary restriction measures, continued comprehensive education, and guidelines to improve in-hospital use of antibiotics and related costs. In a short-term analysis, total antibiotic consumption per patient admitted, which was expressed as defined daily doses (DDD), decreased by 36% (P < .001), and intravenous DDDs decreased by 46% (P < .01). Overall expenditures for antibiotic treatment decreased by 53% (US$100 per patient admitted). The 2 main cost-lowering factors were a reduction in prescription of antibiotics (35% fewer treatments; P < .0001) and more diligent use of 5 broad-spectrum antibiotics (23% vs. 10% of treatments; P = .001). Quality of care was not compromised. A pharmacy-based, prospective, long-term surveillance of DDDs and costs over 4 years showed an ongoing effect. This comprehensive intervention program, which aimed to reduce antibiotic consumption and costs, was highly successful and had long-lasting effect

Recurrent post‐partum seizures after epidural blood patch

There are many causes for headaches after childbirth. Even though postdural puncture headache (PDPH) has to be considered in a woman with a history of difficult epidural anaesthesia, pre‐eclampsia should always be excluded as an important differential diagnosis. We report a case with signs of late‐onset pre‐eclampsia where administration of an epidural blood patch (EBP) was associated with eclampsia. A hypothetical causal relationship between the EBP and seizures was discarded on the basis of evidence presented in this report. Br J Anaesth 2003; 90: 247-5