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On unitary convex decompositions of vectors in a J B * -algebra

Akhlaq A. Siddiqui — 2013

Archivum Mathematicum

By exploiting his recent results, the author further investigates the extent to which variation in the coefficients of a unitary convex decomposition of a vector in a unital J B * -algebra permits the vector decomposable as convex combination of fewer unitaries; certain C * -algebra results due to M. Rørdam have been extended to the general setting of J B * -algebras.

Asymmetric decompositions of vectors in J B * -algebras

Akhlaq A. Siddiqui — 2006

Archivum Mathematicum

By investigating the extent to which variation in the coefficients of a convex combination of unitaries in a unital J B * -algebra permits that combination to be expressed as convex combination of fewer unitaries of the same algebra, we generalise various results of R. V. Kadison and G. K. Pedersen. In the sequel, we shall give a couple of characterisations of J B * -algebras of t s r 1 .

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