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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.

Functional analytic characterization of classes of convex bodies.

P. Goodey, E. Lutwak, W. Weil (1996)

Mathematische Zeitschrift

Generalized moment problem in vector lattices.

Duchon, Miloslav, Riečan, Beloslav (1996)

Novi Sad Journal of Mathematics

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) $∥ a b ∥ \leq ∥ a ∥ ∥ b ∥$ , $a, b \in 𝔐$ (ii) $∥ a^{2} ∥ = ∥ a ∥^{2}$ (iii) $∥ a^{2} ∥ \leq ∥ a^{2} + b^{2} ∥$ . $𝔐$ 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...

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Extreme extensions of positive operators

Extreme extensions of positive operators, II

Faces complémentables dans un cône

Faserungen von Fahnenmengen

FF-Banachverbandsalgebren.

Fixed points of semigroups of positive operators in KB-spaces

Fortsetzungen extremaler Funktionale.

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

Functional analytic characterization of classes of convex bodies.

Generalized moment problem in vector lattices.

Homogeneous self dual cones versus Jordan algebras. The theory revisited

Inclusion Statements for Operator Equations by a Continuity Principle.

Inductive limits and tensor products of ordered topological vector spaces and algebras

Infinitely divisible measures on the cone of an ordered locally convex vector spaces

Injective Banach Lattices.

Integral representations of non-linear functionals

Invariant metrics on convex cones

Inverses and regularity of disjointness preserving operators [Book]

Isomorphismes bicroissants des cônes convexes.

Isomorphismes bicroissants des cônes convexes

Currently displaying 101 – 120 of 422