On the Geometry of the Unit Ball of a JB*-Triple
, Haifa M. Tahlawi, Akhlaq A. Siddiqui, and Fatmah B. Jamjoom . 2013
We explore a JB^{∗}-triple analogue of the notion of quasi invertible elements, originally studied by L. Brown and G. 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 Neuamnn 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 R. Kadison and G. Pedersen, M. Rørdam, L. Brown, J. Wright and M. Youngson and A. Siddiqui, including the Russo-Dye theorem are extended to JB^{∗}-trip
We discuss the λ-function in the general setting of JB∗-triples. Several results connecting the λ-function with the distance of a vector to the Brown–Pedersen’s quasi-invertible elements and…
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It is well known (see[9, 11.2.18]) that if A and B are maximal abelian von Neumann subalgebras of von Neumann algebras M and N, respectively, then A⊗B is a maximal abelian von Neumann subalgebra…