Page 1

Displaying 1 – 6 of 6

Showing per page

Holomorphic automorphisms and collective compactness in J*-algebras of operator

José Isidro (2007)

Open Mathematics

Let G be the Banach-Lie group of all holomorphic automorphisms of the open unit ball B 𝔄 in a J*-algebra 𝔄 of operators. Let 𝔉 be the family of all collectively compact subsets W contained in B 𝔄 . We show that the subgroup F ⊂ G of all those g ∈ G that preserve the family 𝔉 is a closed Lie subgroup of G and characterize its Banach-Lie algebra. We make a detailed study of F when 𝔄 is a Cartan factor.

Holomorphic retractions and boundary Berezin transforms

Jonathan Arazy, Miroslav Engliš, Wilhelm Kaup (2009)

Annales de l’institut Fourier

In an earlier paper, the first two authors have shown that the convolution of a function f continuous on the closure of a Cartan domain and a K -invariant finite measure μ on that domain is again continuous on the closure, and, moreover, its restriction to any boundary face F depends only on the restriction of f to F and is equal to the convolution, in  F , of the latter restriction with some measure μ F on F uniquely determined by  μ . In this article, we give an explicit formula for μ F in terms of  F ,...

Homogeneous self dual cones versus Jordan algebras. The theory revisited

Jean Bellissard, B. Iochum (1978)

Annales de l'institut Fourier

Let 𝔐 be a Jordan-Banach algebra with identity 1, whose norm satisfies:(i) a b a b ,    a , b 𝔐 (ii) a 2 = a 2 (iii) a 2 a 2 + b 2 . 𝔐 is called a JB algebra (E.M. Alfsen, F.W. Shultz and E. Stormer, Oslo preprint (1976)). The set 𝔐 + of squares in 𝔐 is a closed convex cone. ( 𝔐 , 𝔐 + , 1 ) is a complete ordered vector space with 1 as a order unit. In addition, we assume 𝔐 to be monotone complete (i.e. 𝔐 coincides with the bidual 𝔐 * * ), and that there exists a finite normal faithful trace φ on 𝔐 .Then the completion { 𝔐 + } φ of 𝔐 + with respect to the Hilbert structure...

Currently displaying 1 – 6 of 6

Page 1