Semi-continuous linear lattices
Semivariation in -spaces
Suppose that and are Banach spaces and that the Banach space is their complete tensor product with respect to some tensor product topology . A uniformly bounded -valued function need not be integrable in with respect to a -valued measure, unless, say, and are Hilbert spaces and is the Hilbert space tensor product topology, in which case Grothendieck’s theorem may be applied. In this paper, we take an index and suppose that and are -spaces with the associated -tensor product...
Sequential closedness of Boolean algebras of projections in Banach spaces
Complete and σ-complete Boolean algebras of projections acting in a Banach space were introduced by W. Bade in the 1950's. A basic fact is that every complete Boolean algebra of projections is necessarily a closed set for the strong operator topology. Here we address the analogous question for σ-complete Boolean algebras: are they always a sequentially closed set for the strong operator topology? For the atomic case the answer is shown to be affirmative. For the general case, we develop criteria...
Silov Boundaries of Spaces of Functions with Noncompact Domains.
Some basic properties of generalized Calderon-Lozanovskiî.
Some characterizations of Banach lattices with the Schur property.
This note contains a short proof of the equivalence of the Schur and Dunford-Pettis properties in the class of discrete KB-spaces. We also present an operator characterization of the Schur property (Theorem 2) and we notice that Banach lattices which band hereditary l1 coincide with Banach lattices having the Schur property. (This characterization is due to Popa (1977)). Moreover, the paper offers examples of Banach lattices with the positive Schur property and without the Schur property and which...
Some characterizations of order weakly compact operator
We introduce the notion of order weakly sequentially continuous lattice operations of a Banach lattice, use it to generalize a result regarding the characterization of order weakly compact operators, and establish its converse. Also, we derive some interesting consequences.
Some characterizations of weakly compact operator on Banach lattices
We establish necessary and sufficient conditions under which each operator between Banach lattices is weakly compact and we give some consequences.
Some problems on narrow operators on function spaces
It is known that if a rearrangement invariant (r.i.) space E on [0, 1] has an unconditional basis then every linear bounded operator on E is a sum of two narrow operators. On the other hand, for the classical space E = L 1[0, 1] having no unconditional basis the sum of two narrow operators is a narrow operator. We show that a Köthe space on [0, 1] having “lots” of nonnarrow operators that are sum of two narrow operators need not have an unconditional basis. However, we do not know if such an r.i....
Some properties of weak Banach-Saks operators
We establish necessary and sufficient conditions under which weak Banach-Saks operators are weakly compact (respectively, L-weakly compact; respectively, M-weakly compact). As consequences, we give some interesting characterizations of order continuous norm (respectively, reflexive Banach lattice).
Some results on Banach spaces without local unconditional structure
Some results on injective Banach lattices
Some results on order weakly compact operators
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.
Some results on the class of -unbounded Dunford-Pettis operators
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.
Stability and ergodicity of dominated semigroups. II. The strong case.
Structure of Cesàro function spaces: a survey
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 .
Structure of Rademacher subspaces in Cesàro type 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 < ∞.
Superconvexity of the Spectral Radius, and Convexity of the Spectral Bound and the Type.
Sur la convergence de polynômes
Sur la convergence forte des moyennes des opérateurs affines positifs