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On the Geometry of the Unit Ball of a -Triple

Author

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  • Haifa M. Tahlawi
  • Akhlaq A. Siddiqui
  • Fatmah B. Jamjoom

Abstract

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.

Suggested Citation

  • Haifa M. Tahlawi & Akhlaq A. Siddiqui & Fatmah B. Jamjoom, 2013. "On the Geometry of the Unit Ball of a -Triple," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, May.
    • Handle: RePEc:hin:jnlaaa:891249
    DOI: 10.1155/2013/891249
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