Dunford-Pettis composition operators on $H^1$ in several variables

Dunford - Pettis Operators 3

If all bounded linear operators from L 1 into a Banach space X are Dunford-Pettis (i.e. carry weakly convergent sequences onto norm convergent sequences), then we say that X has the complete continuity property (CCP). The CCP is a weakening of the Radon-Nikod ym property (RNP). Basic results of Bourgain and Talagrand began to suggest the possibility that the CCP, like the RNP, can be realized a...

Order Almost Dunford-Pettis Operators on Banach Lattices

By introducing the concepts of order almost Dunford-Pettis and almost weakly limited operators in Banach lattices, we give some properties of them related to some well known classes of operators, such as, order weakly compact, order Dunford-Pettis, weak and almost Dunford- Pettis and weakly limited operators. Then, we characterize Banach lat- tices E and F on which each operator from E into F t...

Duality Property for Positive Weak Dunford-Pettis Operators

Power Bounded Composition Operators in Several Variables

Let φ be an analytic self-map of the open unit polydisk D , N ∈ N. Such a map induces a composition operator Cφ acting on weighted Banach spaces of holomorphic functions. We study when such operators are power bounded resp. uniformly mean ergodic. Mathematics Subject Classification (2010): 47B33, 47B38

The Dunford-pettis Property on Tensor Products

We show that, in some cases, the projective and the injective tensor products of two Banach spaces do not have the Dunford-Pettis property (DPP). As a consequence, we obtain that (c0⊗̂πc0)∗∗ fails the DPP. Since (c0⊗̂πc0)∗ does enjoy it, this provides a new space with the DPP whose dual fails to have it. We also prove that, if E and F are L1-spaces, then E⊗̂ǫF has the DPP if and only if both E and...