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The density property for JB*-triples

Seán Dineen, Michael Mackey, Pauline Mellon (1999)

Studia Mathematica

We obtain conditions on a JB*-algebra X so that the canonical embedding of X into its associated quasi-invertible manifold has dense range. We prove that if a JB* has this density property then the quasi-invertible manifold is homogeneous for biholomorphic mappings. Explicit formulae for the biholomorphic mappings are also given.

The geometry of null systems, Jordan algebras and von Staudt's theorem

Wolfgang Bertram (2003)

Annales de l’institut Fourier

We characterize an important class of generalized projective geometries ( X , X ' ) by the following essentially equivalent properties: (1) ( X , X ' ) admits a central null-system; (2) ( X , X ' ) admits inner polarities: (3) ( X , X ' ) is associated to a unital Jordan algebra. These geometries, called of the first kind, play in the category of generalized projective geometries a rôle comparable to the one of the projective line in the category of ordinary projective geometries. In this general set-up, we prove an analogue of von Staudt’s...

The group of commutativity preserving maps on strictly upper triangular matrices

Deng Yin Wang, Min Zhu, Jianling Rou (2014)

Czechoslovak Mathematical Journal

Let 𝒩 = N n ( R ) be the algebra of all n × n strictly upper triangular matrices over a unital commutative ring R . A map ϕ on 𝒩 is called preserving commutativity in both directions if x y = y x ⇔ ϕ ( x ) ϕ ( y ) = ϕ ( y ) ϕ ( x ) . In this paper, we prove that each invertible linear map on 𝒩 preserving commutativity in both directions is exactly a quasi-automorphism of 𝒩 , and a quasi-automorphism of 𝒩 can be decomposed into the product of several standard maps, which extains the main result of Y. Cao, Z. Chen and C. Huang (2002) from fields to rings.

The Kadec-Pełczyński-Rosenthal subsequence splitting lemma for JBW*-triple preduals

Antonio M. Peralta, Hermann Pfitzner (2015)

Studia Mathematica

Any bounded sequence in an L¹-space admits a subsequence which can be written as the sum of a sequence of pairwise disjoint elements and a sequence which forms a uniformly integrable or equiintegrable (equivalently, a relatively weakly compact) set. This is known as the Kadec-Pełczyński-Rosenthal subsequence splitting lemma and has been generalized to preduals of von Neuman algebras and of JBW*-algebras. In this note we generalize it to JBW*-triple preduals.

The structure and representation of n-ary algebras of DNA recombination

Sergei Sverchkov (2011)

Open Mathematics

In this paper we investigate the structure and representation of n-ary algebras arising from DNA recombination, where n is a number of DNA segments participating in recombination. Our methods involve a generalization of the Jordan formalization of observables in quantum mechanics in n-ary splicing algebras. It is proved that every identity satisfied by n-ary DNA recombination, with no restriction on the degree, is a consequence of n-ary commutativity and a single n-ary identity of the degree 3n-2....

The triple-norm extension problem: the nondegenerate complete case.

A. Moreno Galindo (1999)

Studia Mathematica

We prove that, if A is an associative algebra with two commuting involutions τ and π, if A is a τ-π-tight envelope of the Jordan Triple System T:=H(A,τ) ∩ S(A,π), and if T is nondegenerate, then every complete norm on T making the triple product continuous is equivalent to the restriction to T of an algebra norm on A.

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