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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 the Lie algebra of holomorphic infinitesimal isometries of some classical complex symmetric Banach manifolds

José Isidro (2007)

Open Mathematics

The Banach-Lie algebras ℌκ of all holomorphic infinitesimal isometries of the classical symmetric complex Banach manifolds of compact type (κ = 1) and non compact type (κ = −1) associated with a complex JB*-triple Z are considered and the Lie ideal structure of ℌκ is studied.

On the radical of J*-triples.

Erhard Neher (1992)

Mathematische Zeitschrift

On the Scole of a Noncommutative Jordan Algebra.

A. Fernandez López, Rodriguez P. A. (1986)

Manuscripta mathematica

On the structure of $A J W$ -algebras of type $I_{2}$ .

Kusraev, A.G. (1999)

Vladikavkazskiĭ Matematicheskiĭ Zhurnal

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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