On the Geometry of the Unit Ball of a JB*-Triple

Journal Article

, Haifa M. Tahlawi, Akhlaq A. Siddiqui, and Fatmah B. Jamjoom . 2013

• نوع عمل المنشور: بحث علمي أصيل
• رابط المنشور على الويب: http://dx.doi.org/10.1155/2013/891249
• المجلة \ الصحيفة: ABSTRACT AND APPLIED ANALYSIS
• رقم العدد: 1
• رقم الإصدار السنوي: 2013
• الصفحات: from 1 to 8

مستخلص المنشور

We explore a JB^{∗}-triple analogue of the notion of quasi invertible elements, originally studied by L. Brown and G. Pedersen in the setting of C^{∗}-algebras. This class of BP-quasi invertible elements properly includes all invertible elements and all extreme points of the unit ball, and is properly included in von Neuamnn regular elements in a JB^{∗}-triple; this indicates their structural richness. We initiate a study of the unit ball of a JB^{∗}-triple investigating some structural properties of the BP-quasi invertible elements; here and in sequent papers, we show that various results on unitary convex decompositions and regular approximations can be extended to the setting of BP-quasi invertible elements. Some C^{∗}-algebra and JB^{∗}-algebra results, due to R. Kadison and G. Pedersen, M. Rørdam, L. Brown, J. Wright and M. Youngson and A. Siddiqui, including the Russo-Dye theorem are extended to JB^{∗}-trip