Search results for " lineable"

showing 2 items of 2 documents

Lineability of non-differentiable Pettis primitives

2014

Let \(X\) be an infinite-dimensional Banach space. In 1995, settling a long outstanding problem of Pettis, Dilworth and Girardi constructed an \(X\)-valued Pettis integrable function on \([0,1]\) whose primitive is nowhere weakly differentiable. Using their technique and some new ideas we show that \(\mathbf{ND}\), the set of strongly measurable Pettis integrable functions with nowhere weakly differentiable primitives, is lineable, i.e., there is an infinite dimensional vector space whose nonzero vectors belong to \(\mathbf{ND}\).

Discrete mathematicsPettis integralMathematics::Functional AnalysisIntegrable systemGeneral MathematicsBanach space46G10 28B05Functional Analysis (math.FA)Mathematics - Functional AnalysisSet (abstract data type)Dvoretzky's theoremFOS: MathematicsLocally integrable functionDifferentiable functionPettis Integral nowhere differentiable Dvoretzky's theorem lineable spaceableMathematicsVector spaceMonatshefte für Mathematik
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Rolewicz-type chaotic operators

2015

In this article we introduce a new class of Rolewicz-type operators in l_p, $1 \le p < \infty$. We exhibit a collection F of cardinality continuum of operators of this type which are chaotic and remain so under almost all finite linear combinations, provided that the linear combination has sufficiently large norm. As a corollary to our main result we also obtain that there exists a countable collection of such operators whose all finite linear combinations are chaotic provided that they have sufficiently large norm.

Pure mathematicsApplied MathematicsExistential quantificationChaoticCardinality of the continuumFunctional Analysis (math.FA)Mathematics - Functional AnalysisCorollary47A16 47B37 37B99Settore MAT/05 - Analisi MatematicaNorm (mathematics)chaotic operators hypercyclic operators lineable Rolewicz operatorFOS: MathematicsCountable setLinear combinationAnalysisMathematics
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