Displaying 101 – 120 of 419

Showing per page

Fréchet-spaces-valued measures and the AL-property.

S. Okada, W. J. Ricker (2003)

RACSAM

Associated with every vector measure m taking its values in a Fréchet space X is the space L1(m) of all m-integrable functions. It turns out that L1(m) is always a Fréchet lattice. We show that possession of the AL-property for the lattice L1(m) has some remarkable consequences for both the underlying Fréchet space X and the integration operator f → ∫ f dm.

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 101 – 120 of 419