Let (Ω,Σ,μ) be a finite measure space and let X be a real Banach space. Let $L^{\Phi }\left(X\right)$ be the Orlicz-Bochner space defined by a Young function Φ. We study the relationships between Dunford-Pettis operators T from L¹(X) to a Banach space Y and the compactness properties of the operators T restricted to $L^{\Phi }\left(X\right)$. In particular, it is shown that if X is a reflexive Banach space, then a bounded linear operator T:L¹(X) → Y is Dunford-Pettis if and only if T restricted to $L^{\infty }\left(X\right)$ is $(\tau (L^{\infty }\left(X\right),L¹(X*)),|\left|·\right|{|}_Y)$-compact.

We investigate the dynamical behavior of the operators of differentiation and integration and the Hardy operator on weighted Banach spaces of entire functions defined by integral norms. In particular we analyze when they are hypercyclic, chaotic, power bounded, and (uniformly) mean ergodic. Moreover, we estimate the norms of the operators and study their spectra. Special emphasis is put on exponential weights.