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On vector measures

Corneliu Constantinescu (1975)

Annales de l'institut Fourier

Let ℳ be the Banach space of real measures on a σ -ring R , let ℳ ' be its dual, let E be a quasi-complete locally convex space, let E ' be its dual, and let μ be an E -valued measure on R . If is shown that for any θ ∈ ℳ ' there exists an element ∫ θ d μ of E such that ⟨ x ' ∘ μ , θ ⟩ = ∫ θ d μ , x ' for any x ' ∈ E ' and that the map θ → ∫ θ d μ : ℳ ' → E is order continuous. It follows that the closed convex hull of μ ( R ) is weakly compact.

Open partial isometries and positivity in operator spaces

David P. Blecher, Matthew Neal (2007)

Studia Mathematica

We first study positivity in C*-modules using tripotents ( = partial isometries) which are what we call open. This is then used to study ordered operator spaces via an "ordered noncommutative Shilov boundary" which we introduce. This boundary satisfies the usual universal diagram/property of the noncommutative Shilov boundary, but with all the arrows completely positive. Because of their independent interest, we also systematically study open tripotents and their properties.

Order bounded orthosymmetric bilinear operator

Elmiloud Chil (2011)

Czechoslovak Mathematical Journal

It is proved by an order theoretical and purely algebraic method that any order bounded orthosymmetric bilinear operator b : E × E → F where E and F are Archimedean vector lattices is symmetric. This leads to a new and short proof of the commutativity of Archimedean almost f -algebras.

Order intervals in C ( K ) . Compactness, coincidence of topologies, metrizability

Zbigniew Lipecki (2022)

Commentationes Mathematicae Universitatis Carolinae

Let K be a compact space and let C ( K ) be the Banach lattice of real-valued continuous functions on K . We establish eleven conditions equivalent to the strong compactness of the order interval [ 0 , x ] in C ( K ) , including the following ones: (i) { x > 0 } consists of isolated points of K ; (ii) [ 0 , x ] is pointwise compact; (iii) [ 0 , x ] is weakly compact; (iv) the strong topology and that of pointwise convergence coincide on [ 0 , x ] ; (v) the strong and weak topologies coincide on [ 0 , x ] . Moreover, the weak topology and that of pointwise convergence...

Orthosymmetric bilinear map on Riesz spaces

Elmiloud Chil, Mohamed Mokaddem, Bourokba Hassen (2015)

Commentationes Mathematicae Universitatis Carolinae

Let E be a Riesz space, F a Hausdorff topological vector space (t.v.s.). We prove, under a certain separation condition, that any orthosymmetric bilinear map T : E × E → F is automatically symmetric. This generalizes in certain way an earlier result by F. Ben Amor [On orthosymmetric bilinear maps, Positivity 14 (2010), 123–134]. As an application, we show that under a certain separation condition, any orthogonally additive homogeneous polynomial P : E → F is linearly represented. This fits in the type of results by...

Currently displaying 201 – 220 of 419