Von Neumann Regularity and Quadratic Conorms in JB^＊-triples and C^＊-algebras

We revise the notion of von Neumann regularity in JB^＊-triples by finding a new characterisation in terms of the range of the quadratic operator Q（a）. We introduce the quadratic conorm of an element a in a JB^＊-triple as the minimum reduced modulus of the mapping Q（a）. It is shown that the quadratic conorm of a coincides with the infimum of the squares of the points in the triple spectrum of a. It is established that a contractive bijection between JBW^＊-triples is a triple isomorphism if, and only if, it preserves quadratic conorms. The continuity of the quadratic conorm and the generalized inverse are discussed. Some applications to C^＊-algebras and von Neumann algebras are also studied.     

The alternative Daugavet property of C *‐algebras and JB *‐triples

A Banach space X is said to have the alternative Daugavet property if for every (bounded and linear) rank‐one operator T: X → X there exists a modulus one scalar ω such that ∥Id+ωT ∥ = 1 + ∥T ∥. We give geometric characterizations of this property in the setting of C *‐algebras, JB *‐triples, and of their isometric preduals. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bicircular projections and characterization of Hilbert spaces

We prove that every JB* triple with rank one bicircular projection is a direct sum of two ideals, one of which is isometrically isomorphic to a Hilbert space.

     

电子碰撞激发产生软X光激光的理论研究

用一维非平衡辐射流体力学程序JB19对激光照射Au、Se、Ge、Cu等靶进行了模拟计算,并对形成的等离子体状态做了详细描述。计算表明只要选取适当的激光介质(包括材料、形状和结构)和相匹配的激光条件就可以得到产生粒子数反转和激光增益的最佳等离子体状态。计算结果与LLNL(劳伦斯利弗莫尔实验室),NRL(海军实验室),CEL(里梅尔实验室)实验观察值符合得很好。     

JB代数中的面结构

本文描述了含单元元的ＪＢ代数及其对偶空间的单位球和这些单位球的正部的闭面。     

Negative refraction in a honeycomb-lattice photonic crystal

In this paper we theoretically investigate a photonic crystal with dielectric rods in a honeycomb lattice. Two left-handed frequency regions are found in the second and third photonic band by using the plane wave expansion method to analyze the photonic band structure and equifrequency contours. Subwavelength imaging by the photonic crystal flat lens are systematically studied by numerical simulations using the multiple scattering method. Different from the photonic crystals with noncircular dielectric rods in air, this structure is almost isotropic at the optimal frequency for superlensing. As a comparison, flat slab focusing is also demonstrated at other frequencies in the two left-handed regions.     

Grothendieck's Inequalities for Real and Complex JBW*-Triples

We prove that, if and >0, if V and W are complex JBW*-triples (with preduals V_* andW_*, respectively), and if U is a separately weak*-continuousbilinear form on V x W, then there exist norm-one functionals₁, ₂ V_* and ₁, ₂ W_* satisfying for all (x, y) V x W. Here, for a norm-one functional on acomplex JB*-triple V, |·| stands for the prehilbertianseminorm on V associated to given by for all x W, where z V^** satisfies z = |z| =1. We arrive at this form of ‘Grothendieck's inequality’through results of C.-H. Chu, B. Iochum, and G. Loupias, andan amended version of the ‘little Grothendieck's inequality’for complex JB*-triples due to T. Barton and Y. Friedman. Wealso obtain extensions of these results to the setting of realJB*-triples. 2000 Mathematical Subject Classification: 17C65,46K70, 46L05, 46L10, 46L70.     

JB9014炸药在常温和-54 ℃低温下冲击引爆压力场发展的实验研究

 应用锰铜压力计对钝感高能炸药JB9014在常温和-54 ℃下冲击起爆压力场的发展进行了实验研究。在-54 ℃下压力场的发展图像揭示出JB9014炸药遵循均质炸药起爆机理,而常温下的这种图像表明其兼备均质和非均质炸药起爆机理;在-54 ℃下JB9014炸药的冲击感度比常温下低得多;无论是在常温下还是在-54 ℃低温下,JB9014炸药的冲击感度均比具有相同TATB/粘结剂配比的PBX-9502炸药的低。     

Operators from the Hardy space to the α‐Bloch space

Let be a bounded symmetric domain realized as the open unit ball of a finite dimensional JB*‐triple X. In this paper, we characterize the bounded weighted composition operators from the Hardy space into the α‐Bloch space on . Also, we show the multiplication operator from into is bounded. Finally, we show that there exist no isometric composition operators.     

On the axiomatic definition of real JB*–triples

In the last twenty years, a theory of real Jordan triples has been developed. In 1994 T. Dang and B. Russo introduced the concept of J*B–triple. These J*B–triples include real C*–algebras and complex JB*–triples. However, concerning J*B–triples, an important problem was left open. Indeed, the question was whether the complexification of a J*B–triple is a complex JB*–triple in some norm extending the original norm. T. Dang and B. Russo solved this problem for commutative J*B–triples. In this paper we characterize those J*B–triples with a unitary element whose complexifications are complex JB*–triples in some norm extending the original one. We actually find a necessary and sufficient new axiom to characterize those J*B–triples with a unitary element which are J*B–algebras in the sense of [1] or real JB*–triples in the sense of [4].