# B. Aqzzouz

Search this author in Google Scholar

Articles: 6

### Dunford-Pettis property of the product of some operators

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

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

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

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

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

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