We explore a -triple analogue of the notion of quasi invertible elements, originally studied by Brown and Pedersen in the setting of -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 -triple; this indicates their structural richness. We initiate a study of the unit ball of a -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 -algebra and -algebra results, due to Kadison and Pedersen, Rørdam, Brown, Wright and Youngson, and Siddiqui, including the Russo-Dye theorem, are extended to -triples.
"On the Geometry of the Unit Ball of a -Triple." Abstr. Appl. Anal. 2013 1 - 8, 2013. https://doi.org/10.1155/2013/891249