On weak non-linearity of models of physical systems

Daniel Mayer; Zdeněk Ryjáček

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A note on weakly $(μ, λ)$ -closed functions

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In this paper we introduce a new class of functions called weakly $(μ, λ)$ -closed functions with the help of generalized topology which was introduced by Á. Császár. Several characterizations and some basic properties of such functions are obtained. The connections between these functions and some other similar types of functions are given. Finally some comparisons between different weakly closed functions are discussed. This weakly $(μ, λ)$ -closed functions enable us to facilitate the formulation...

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An alternative Dunford-Pettis Property

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An alternative to the Dunford-Pettis Property, called the DP1-property, is introduced. Its relationship to the Dunford-Pettis Property and other related properties is examined. It is shown that $ℓ_{p}$ -direct sums of spaces with DP1 have DP1 if 1 ≤ p < ∞. It is also shown that for preduals of von Neumann algebras, DP1 is strictly weaker than the Dunford-Pettis Property, while for von Neumann algebras, the two properties are equivalent.