Abstract and Applied Analysis

On the Geometry of the Unit Ball of a J B * -Triple

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

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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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Abstr. Appl. Anal., Volume 2013 (2013), Article ID 891249, 8 pages.

First available in Project Euclid: 27 February 2014

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Tahlawi, Haifa M.; Siddiqui, Akhlaq A.; Jamjoom, Fatmah B. On the Geometry of the Unit Ball of a $J{B}^{\mathrm{*}}$ -Triple. Abstr. Appl. Anal. 2013 (2013), Article ID 891249, 8 pages. doi:10.1155/2013/891249. https://projecteuclid.org/euclid.aaa/1393511914

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