This paper contains the following results for ecohomies with infinite dimensional commodity spaces. (i) We establish a core-Walras equivalence theorem for economies with an atomless measure space of agents and with an ordered separable Banach commodity space whose positive cone has a non-empty norm interior. This result includes as a special case the Aumann (1964) and Schmeidler-Hildenbrand [Hi...

New characterizations of strictly singular operators between Banach lattices are given. It is proved that, for Banach lattices X and Y such that X has finite cotype and Y satisfies a lower 2-estimate, an operator T : X → Y is strictly singular if and only if it is disjointly strictly singular and 2-singular. Moreover, if T is regular then the same equivalence holds provided that Y is just order...

We prove existence results for discontinuous functional equations in general L-spaces and apply these results to the solvability of implicit and explicit elliptic boundary-value problems involving discontinuous nonlinearities. The main tool in the proof is a fixed point result in lattice-ordered Banach spaces proved by the second author.

In this note, we describe the generator of the modulus semigroup of the C0-semigroup associated with the delay equation { u′(t) = Au(t) + Lut, t > 0, u(0) = x ∈ R, u0 = f ∈ L(−h, 0;R) , in the Banach lattice R × L(−h, 0;R). MCS 2000: 34K06

We prove that if X is an infinite dimensional Banach lattice with a weak unit then there exists a probability space (Ω,Σ, μ) so that the unit sphere S(L1(Ω,Σ, μ) is uniformly homeomorphic to the unit sphere S(X) if and only if X does not contain l ∞’s uniformly.

Let E be a Banach lattice, T be a bounded operator on E. The Weyl essential spectrum σew(T ) of the operator T is a set σew(T ) = ∩ K∈K(E) σ(T + K), where K(E) is a set of all compact operators on E. In particular for a positive operator T next subsets of the spectrum

Abstract In this note we consider the order Lozanovsky spectrum of a positive operator on complex Banach lattice and show that it generally contains Weyl spectrum, settling weaker form question raised in Alekhno (Positivity 13(1):3–20, 2009).

In this paper we first prove a rather general theorem about existence of solutions for an abstract differential equation in a Banach space by assuming that the nonlinear term is in some sense weakly continuous. We then apply this result to a lattice dynamical system with delay, proving also the existence of a global compact attractor for such system.

Using a fixed point theorem in ordered Banach spaces with lattice structure founded by Liu and Sun, this paper investigates the multiplicity of nontrivial solutions for fourth order m-point boundary value problems with sign-changing nonlinearity. Our results are new and improve on those in the literature.

Let X be a completely regular Hausdorff space, E a Banach lattice, and μ an E-valued countably additive, regular Borel measure on X. Some results about the countable additivity and regularity of the modulus |μ| are proved. Also in special cases, it is proved that L1(μ) = L1(|μ|).