Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Nonassociative normed algebras: geometric aspects

100%

Palacios A. R.

Banach Center Publications

1994

tom 30

nr 1

299-311

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 a general nonassociative normed algebra, imply that the algebra is actually "nearly associative". We shall explain this idea by selecting four favourite topics, namely: • Nonassociative Vidav-Palmer theorem, • Nonassociative Gelfand-Naimark theorem, • Nonassociative smooth normed algebras, and • One-sided division absolute valued algebras. Although there are classical nice forerunners in this circle of ideas, as for example the Albert-Urbanik-Wright determination of (nonassociative) absolute valued algebras with a unit ([2], [3], [42], and [41]), a systematic treatment of questions of this type has been made only recently, more precisely since 1980 [34].

On the behaviour of Jordan-algebra norms on associative algebras

51%

Cabrera Garcia M., Galindo A. M., Palacios A. R.

Studia Mathematica

1995

tom 113

nr 1

81-100

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 and the normed versions of Zel'manov's prime theorem for Jordan algebras are discussed.

Ograniczanie wyników

1 Banach Center Publications

1 Studia Mathematica

2 Palacios A. R.

1 Cabrera Garcia M.

1 Galindo A. M.

1 1995

1 1994

Wyniki wyszukiwania

Nonassociative normed algebras: geometric aspects

On the behaviour of Jordan-algebra norms on associative algebras