Displaying similar documents to “A characterization of commutativity for non-associative normed algebras.”

Nonassociative normed algebras: geometric aspects

Angel Rodríguez Palacios (1994)

Banach Center Publications

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Introduction. The aim of this paper is to review some relevant results concerning the geometry of nonassociative normed algebras, without assuming in the first instance that such algebras satisfy any familiar identity, like associativity, commutativity, or Jordan axiom. In the opinion of the author, the most impressive fact in this direction is that most of the celebrated natural geometric conditions that can be required for associative normed algebras, when imposed on...

One-sided division absolute valued algebras.

Ana Rodríguez Palacios (1992)

Publicacions Matemàtiques

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We develop a structure theory for left divsion absolute valued algebras which shows, among other things, that the norm of such an algebra comes from an inner product. Moreover, we prove the existence of left division complete absolute valued algebras with left unit of arbitrary infinite hilbertian division and with the additional property that they have nonzero proper closed left ideals. Our construction involves results from the representation theory of the so called "Canonical Anticommutation...

ANOVA using commutative Jordan algebras, an application

Paulo Canas Rodrigues, João Tiago Mexia (2006)

Discussiones Mathematicae Probability and Statistics

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Binary operations on commutative Jordan algebras are used to carry out the ANOVA of a two layer model. The treatments in the first layer nests those in the second layer, that being a sub-model for each treatment in the first layer. We present an application with data retried from agricultural experiments.

On the behaviour of Jordan-algebra norms on associative algebras

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

Studia Mathematica

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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...

Canonic inference and commutative orthogonal block structure

Francisco P. Carvalho, João Tiago Mexia, M. Manuela Oliveira (2008)

Discussiones Mathematicae Probability and Statistics

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It is shown how to define the canonic formulation for orthogonal models associated to commutative Jordan algebras. This canonic formulation is then used to carry out inference. The case of models with commutative orthogonal block structures is stressed out.