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In this note we prove that there exists a Carathéodory vector lattice $V$ such that $V ≅ V^{3}$ and $V ≇ V^{2}$ . This yields that $V$ is a solution of the Schröder-Bernstein problem for Carathéodory vector lattices. We also show that no Carathéodory Banach lattice is a solution of the Schröder-Bernstein problem.

On the sequential order continuity of the $C (K)$ -space.

Ercan, Zafer, Önal, Suleyman (2007)

Sibirskij Matematicheskij Zhurnal

On the support of midconvex operators.

Kazimierz Nikodem (1991)

Aequationes mathematicae

On the support of midconvex operators. (Summary).

Kazimierz Nikodem (1991)

Aequationes mathematicae

On the upper envelopes of a family of $n$ -disjoint operators.

Radnaev, V.A. (2001)

Vladikavkazskiĭ Matematicheskiĭ Zhurnal

On vector lattices of elementary Carathéodory functions

Ján Jakubík (2005)

Czechoslovak Mathematical Journal

In this paper we deal with the vector lattice $C (B)$ of all elementary Carathéodory functions corresponding to a generalized Boolean algebra $B$ .

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 $θ \in ℳ^{'}$ there exists an element $\int θ d μ$ of $E$ such that $⟨ x^{'} \circ μ, θ ⟩ = ⟨\int θ d μ, x^{'}⟩$ for any $x^{'} \in E^{'}$ and that the map $θ \to \int θ d μ : ℳ^{'} \to E$ 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 $b : E \times E \to F$ 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...

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Displaying 41 – 60 of 63

On the extension of positive operators

On the Integral Representation in Convex Noncompact Sets of Tight Measures.

On the order-topological properties of the quotient space $L / L_{A}$

On the o-Spectrum of Order Bounded Operators.

On the Representation of Banach Lattices by Continuous Numerical Functions.

On the representation of Orlicz lattices

On the Schröder-Bernstein problem for Carathéodory vector lattices