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Modes of ideal continuity and the additive property in the Riesz space setting

Boccuto A., Dimitriou X., Papanastassiou N., Wilczyński W.

Journal of Applied Analysis

2014

Vol. 20, nr 1

41--53

In this paper we present some different types of ideal convergence/divergence and of ideal continuity for Riesz space-valued functions, and prove some basic properties and comparison results. We investigate the relations among different modes of ideal continuity and present a characterization of the (AP)-property for ideals of an abstract set Λ. Finally we pose some open problems.

Modes of (α)-convergence of sequences of functions

Athanassiadou E., Boccuto A., Papanastassiou N.

Commentationes Mathematicae

2013

Vol 53, No. 1

83--94

In this paper we deal with continuous convergence and some related properties of sequences of functions. We present some conditions to get uniform convergence of the sequence involved to a constant function. As an application, we give a result on equivalence between modes of convergence.

Unconditional convergence in lattice groups with respect to ideals

Boccuto A., Dimitriou X., Papanastassiou N.

Commentationes Mathematicae

2010

Vol. 50, [Z] 2

161-174

We deal with unconditional convergence of series and some special classes of subsets of N.