Open Access
2013 On the Geometry of the Unit Ball of a J B * -Triple
Haifa M. Tahlawi, Akhlaq A. Siddiqui, Fatmah B. Jamjoom
Abstr. Appl. Anal. 2013: 1-8 (2013). DOI: 10.1155/2013/891249


We explore a J B * -triple analogue of the notion of quasi invertible elements, originally studied by Brown and 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 Neumann regular elements in a J B * -triple; this indicates their structural richness. We initiate a study of the unit ball of a J B * -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 J B * -algebra results, due to Kadison and Pedersen, Rørdam, Brown, Wright and Youngson, and Siddiqui, including the Russo-Dye theorem, are extended to J B * -triples.


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Haifa M. Tahlawi. Akhlaq A. Siddiqui. Fatmah B. Jamjoom. "On the Geometry of the Unit Ball of a J B * -Triple." Abstr. Appl. Anal. 2013 1 - 8, 2013.


Published: 2013
First available in Project Euclid: 27 February 2014

zbMATH: 07095462
MathSciNet: MR3064400
Digital Object Identifier: 10.1155/2013/891249

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
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