Displaying similar documents to “Homogeneous self dual cones versus Jordan algebras. The theory revisited”

A structure theory for Jordan H * -pairs

A. J. Calderón Martín, C. Martín González (2004)

Bollettino dell'Unione Matematica Italiana

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Jordan H * -pairs appear, in a natural way, in the study of Lie H * -triple systems ([3]). Indeed, it is shown in [4, Th. 3.1] that the problem of the classification of Lie H * -triple systems is reduced to prove the existence of certain L * -algebra envelopes, and it is also shown in [3] that we can associate topologically simple nonquadratic Jordan H * -pairs to a wide class of Lie H * -triple systems and then the above envelopes can be obtained from a suitable classification, in terms of associative...

Supporting sequences of pure states on JB algebras

Jan Hamhalter (1999)

Studia Mathematica

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We show that any sequence ( φ n ) of mutually orthogonal pure states on a JB algebra A such that ( φ n ) forms an almost discrete sequence in the relative topology induced by the primitive ideal space of A admits a sequence ( a n ) consisting of positive, norm one, elements of A with pairwise orthogonal supports which is supporting for ( φ n ) in the sense of φ n ( a n ) = 1 for all n. Moreover, if A is separable then ( a n ) can be taken such that ( φ n ) is uniquely determined by the biorthogonality condition φ n ( a n ) = 1 . Consequences of this...

On annihilators in Jordan algebras.

Antonio Fernández López (1992)

Publicacions Matemàtiques

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In this paper we prove that a nondegenerate Jordan algebra satisfying the descending chain condition on the principal inner ideals, also satisfies the ascending chain condition on the annihilators of the principal inner ideals. We also study annihilators in Jordan algebras without nilpotent elements and in JB-algebras.

A new proof of the noncommutative Banach-Stone theorem

David Sherman (2006)

Banach Center Publications

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Surjective isometries between unital C*-algebras were classified in 1951 by Kadison [K]. In 1972 Paterson and Sinclair [PS] handled the nonunital case by assuming Kadison’s theorem and supplying some supplementary lemmas. Here we combine an observation of Paterson and Sinclair with variations on the methods of Yeadon [Y] and the author [S1], producing a fundamentally new proof of the structure of surjective isometries between (nonunital) C*-algebras. In the final section we indicate...

On the range of a normal Jordan * -derivation

Lajos Molnár (1994)

Commentationes Mathematicae Universitatis Carolinae

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In this note, by means of the spectrum of the generating operator, we characterize the self-adjointness and closedness of the range of a normal and a self-adjoint Jordan *-derivation, respectively.

A Kleinecke-Shirokov type condition with Jordan automorphisms

Matej Brešar, Ajda Fošner, Maja Fošner (2001)

Studia Mathematica

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Let φ be a Jordan automorphism of an algebra . The situation when an element a ∈ satisfies 1 / 2 ( φ ( a ) + φ - 1 ( a ) ) = a is considered. The result which we obtain implies the Kleinecke-Shirokov theorem and Jacobson’s lemma.