B. Aqzzouz

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Articles: 6

Dunford-Pettis property of the product of some operators

Belmesnaoui Aqzzouz, Othman Aboutafail, Aziz Elbour

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 17 (2011), no. 4, 295-299

We establish a sufficient condition under which the product of an order bounded almost Dunford-Pettis operator and an order weakly compact operator is Dunford-Pettis. And we derive some consequences.

Complement on order weakly compact operators

Belmesnaoui Aqzzouz, Jawad H'mishane

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 17 (2011), no. 2, 112-117

We generalize a result on the duality property for order weakly compact operators and use it to establish some characterizations of positive operators.

On some sublattices of regular operators on Banach lattices

Belmesnaoui Aqzzouz, Redouane Nouira

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 14 (2008), no. 4, 297-301

We give some sufficient conditions under which the linear span of positive compact (resp. Dunford-Pettis, weakly compact, AM-compact) operators cannot be a vector lattice without being a sublattice of the order complete vector lattice of all regular operators. Also, some interesting consequences are obtained.

The $\varepsilon_{\infty}$-product of a $b$-space by a quotient bornological space

Belmesnaoui Aqzzouz

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 13 (2007), no. 3, 211-222

We define the $\varepsilon_{\infty }$-product of a Banach space $G$\ by a quotient bornological space $E\mid F$ that we denote by $G\varepsilon _{\infty }(E\mid F)$, and we prove that $G$ is an $% \mathcal{L}_{\infty }$-space if and only if the quotient bornological spaces $G\varepsilon _{\infty }(E\mid F)$ and $% (G\varepsilon E)\mid (G\varepsilon F)$ are isomorphic. Also, we show that the functor $\mathbf{.\varepsilon }_{\infty }\mathbf{.}:\mathbf{Ban\times qBan\longrightarrow qBan}$ is left exact. Finally, we define the $\varepsilon _{\infty }$-product of a b-space by a quotient bornological space and we prove that if $G$ is an $% \varepsilon $b-space\ and $E\mid F$ is a quotient bornological space, then $(G\varepsilon E)\mid (G\varepsilon F)$ is isomorphic to $G\varepsilon _{\infty }(E\mid F)$.

Some results on the space of holomorphic functions taking their values in b-spaces

B. Aqzzouz, M. T. Belghiti, M. H. Elalj, R. Nouira

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 12 (2006), no. 2, 113-123

We define a space of holomorphic functions $O_{1}(U,E/F)$, where $U$ is an open pseudo-convex subset of $\Bbb{C}^{n}$, $E$ is a b-space and $F$ is a bornologically closed subspace of $E$, and we prove that the b-spaces $O_{1}(U,E/F)$ and $O(U,E)/O(U,F)$ are isomorphic.

Bartle and Graves theorem for approximatively surjective mappings with values in $b$-spaces

Belmesnaoui Aqzzouz, Redouane Nouira

Methods Funct. Anal. Topology 11 (2005), no. 4, 320-326


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