We establish some properties of the class of order weakly compact operators on Banach lattices. As consequences, we obtain some characterizations of Banach lattices with order continuous norms or whose topological duals have order continuous norms.
We introduce and study the class of unbounded Dunford--Pettis operators. As consequences, we give basic properties and derive interesting results about the duality, domination problem and relationship with other known classes of operators.
Geometric structure of Cesàro function spaces , where I = [0,1] and [0,∞), is investigated. Among other matters we present a description of their dual spaces, characterize the sets of all q ∈ [1,∞] such that contains isomorphic and complemented copies of -spaces, show that Cesàro function spaces fail the fixed point property, give a description of subspaces generated by Rademacher functions in spaces .
The structure of the closed linear span of the Rademacher functions in the Cesàro space is investigated. It is shown that every infinite-dimensional subspace of either is isomorphic to l₂ and uncomplemented in , or contains a subspace isomorphic to c₀ and complemented in . The situation is rather different in the p-convexification of if 1 < p < ∞.
In this paper it is shown that if a Banach lattice contains a copy of , then it contains an almost lattice isometric copy of . The above result is a lattice version of the well-known result of James concerning the almost isometric copies of in Banach spaces.
We characterize Banach lattices on which every weak Banach-Saks operator is b-weakly compact.
This paper will consider the closure of the set of operators which may be expressed as a sum of lattice homomorphisms whose range is contained in a Dedekind complete Banch lattice.
A sufficient and necessary condition for weak convergence of sequences in a class of Banach sequence lattices is obtained. As a direct application, a complete criterion of a weak convergence of sequences in l infinity is formulated.
In Agbeko (2012) the Hyers-Ulam-Aoki stability problem was posed in Banach lattice environments with the addition in the Cauchy functional equation replaced by supremum. In the present note we restate the problem so that it relates not only to supremum but also to infimum and their various combinations. We then propose some sufficient conditions which guarantee its solution.