APPROXIMATION AND CONVEX DECOMPOSITION BY EXTREMALS AND THE LAMBDA FUNCTION IN JBW*-TRIPLES

Journal Article

, Fatmah Jamjoom, A. Peralta, A. Siddiqui, H. Tahlawi . 2015

• نوع عمل المنشور: بحث علمي
• رابط المنشور على الويب: Approximation and Convex Decomposition by Extremals
• المجلة \ الصحيفة: The Quarterly Journal of Mathematics
• رقم العدد: 2015
• رقم الإصدار السنوي: 2015
• الصفحات: من 1 إلى 21

مستخلص المنشور

We establish new estimates to compute the λ-function of Aron and Lohman on the unit ball of a JB*-triple. It is established that for every Brown--Pedersen quasi-invertible element a in a JB*-triple E we have dist(a,Ԑ(E₁))=max{1-m_{q}(a),‖a‖-1} , where Ԑ(E₁) denotes the set of extreme points of the closed unit ball E₁ of E. It is proved that λ(a)=(1+m_{q}(a))/2 , for every Brown--Pedersen quasi-invertible element a in E₁, where m_{q}(a) is the square root of the quadratic conorm of a. For an element a in E₁ which is not Brown--Pedersen quasi-invertible, we can only estimate that λ(a)≤(1-α_{q}(a))/2). A complete description of the λ-function on the closed unit ball of every JBW*-triple is also provided, and as a consequence, we prove that every JBW*-triple satisfies the uniform λ-property.