On Pettis integrability

Juan Carlos Ferrando

Displaying similar documents to “On Pettis integrability”

Embedding $c_{0}$ in $bvca (Σ, X)$

Juan Carlos Ferrando, L. M. Sánchez Ruiz (2007)

Czechoslovak Mathematical Journal

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If $(Ω, Σ)$ is a measurable space and $X$ a Banach space, we provide sufficient conditions on $Σ$ and $X$ in order to guarantee that $b v c a (Σ, X)$ , the Banach space of all $X$ -valued countably additive measures of bounded variation equipped with the variation norm, contains a copy of $c_{0}$ if and only if $X$ does.

On the class of order Dunford-Pettis operators

Khalid Bouras, Abdelmonaim El Kaddouri, Jawad H&#039;michane, Mohammed Moussa (2013)

Mathematica Bohemica

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We characterize Banach lattices $E$ and $F$ on which the adjoint of each operator from $E$ into $F$ which is order Dunford-Pettis and weak Dunford-Pettis, is Dunford-Pettis. More precisely, we show that if $E$ and $F$ are two Banach lattices then each order Dunford-Pettis and weak Dunford-Pettis operator $T$ from $E$ into $F$ has an adjoint Dunford-Pettis operator $T^{'}$ from $F^{'}$ into $E^{'}$ if, and only if, the norm of $E^{'}$ is order continuous or $F^{'}$ has the Schur property. As a consequence we show that, if $E$ and $F$ are...

Product of vector measures on topological spaces

Surjit Singh Khurana (2008)

Commentationes Mathematicae Universitatis Carolinae

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For $i = (1, 2)$ , let $X_{i}$ be completely regular Hausdorff spaces, $E_{i}$ quasi-complete locally convex spaces, $E = E_{1} \overset{˘}{\otimes} E_{2}$ , the completion of the their injective tensor product, $C_{b} (X_{i})$ the spaces of all bounded, scalar-valued continuous functions on $X_{i}$ , and $μ_{i}$ $E_{i}$ -valued Baire measures on $X_{i}$ . Under certain conditions we determine the existence of the $E$ -valued product measure $μ_{1} \otimes μ_{2}$ and prove some properties of these measures.

A note on copies of $c_{0}$ in spaces of weak* measurable functions

Juan Carlos Ferrando (2000)

Commentationes Mathematicae Universitatis Carolinae

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If $(Ω, Σ, μ)$ is a finite measure space and $X$ a Banach space, in this note we show that $L_{w^{*}}^{1} (μ, X^{*})$ , the Banach space of all classes of weak* equivalent $X^{*}$ -valued weak* measurable functions $f$ defined on $Ω$ such that $∥ f (ω) ∥ \leq g (ω)$ a.e. for some $g \in L_{1} (μ)$ equipped with its usual norm, contains a copy of $c_{0}$ if and only if $X^{*}$ contains a copy of $c_{0}$ .

Copies of $ℓ_{\infty}$ in the space of Pettis integrable functions with integrals of finite variation

Juan Carlos Ferrando (2012)

Studia Mathematica

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Let (Ω,Σ,μ) be a complete finite measure space and X a Banach space. We show that the space of all weakly μ-measurable (classes of scalarly equivalent) X-valued Pettis integrable functions with integrals of finite variation, equipped with the variation norm, contains a copy of $ℓ_{\infty}$ if and only if X does.

Displaying similar documents to “On Pettis integrability”

Embedding c 0 in bvca ( Σ , X )

On the class of order Dunford-Pettis operators

Product of vector measures on topological spaces

A note on copies of c 0 in spaces of weak* measurable functions

Copies of ℓ ∞ in the space of Pettis integrable functions with integrals of finite variation

Embedding $c_{0}$ in $bvca (Σ, X)$

A note on copies of $c_{0}$ in spaces of weak* measurable functions

Copies of $ℓ_{\infty}$ in the space of Pettis integrable functions with integrals of finite variation