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On the behaviour of Jordan-algebra norms on associative algebras

Miguel Cabrera Garcia, Antonio Moreno Galindo, Angel Rodríguez Palacios (1995)

Studia Mathematica

We prove that for a suitable associative (real or complex) algebra which has many nice algebraic properties, such as being simple and having minimal idempotents, a norm can be given such that the mapping (a,b) ↦ ab + ba is jointly continuous while (a,b) ↦ ab is only separately continuous. We also prove that such a pathology cannot arise for associative simple algebras with a unit. Similar results are obtained for the so-called "norm extension problem", and the relationship between these results...

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.

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