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

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

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: We explore a JB*‐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 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 Kadison and Pedersen, Rørdam, Brown, Wright and Youngson, and Siddiqui, including the Russo‐Dye theorem, are extended to JB*‐triples.

Date: 2013
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https://doi.org/10.1155/2013/891249

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:891249

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