Zbigniew Lipecki

Ph. D.: IM PAN 1973, habilitation: IM PAN 1985

My areas of research are measure theory, functional analysis and operator theory. I am also interested in the history of 20th century mathematics. I am mainly concerned with extending additive functions on algebras of sets and operators on vector lattices, and with constructions and properties of dense subspaces [resp. sublattices] of topological vector spaces [resp. lattices]. Some of my results on these subjects are included in several books and monographs (e.g., C. D. Aliprantis and O. Burkinshaw, Positive Operators, Academic Press, 1985; P. Pérez Carreras and J. Bonet, Barrelled Locally Convex Spaces, North-Holland, 1987).

Part of my work is devoted to the variation and semivariations of an additive function defined on a Boolean algebra and taking values in a Banach space or an Abelian normed group.

I participated in the editorial work of Colloquium Mathematicum (1973-74). I was engaged in the publication of W. Sierpiński's Oeuvres choisies (1974-76) and Selected Papers of Antoni Zygmund (1989). I was one of the editors of E. Marczewski's Collected Mathematical Papers (1996).

Profesional Affiliations and Activities:

Referee for many Polish and foreign mathematical journals, reviewer for Mathematical Reviews (1976--2004) and Zentralblatt für Mathematik (1981--2016).

New Publications:

• Semivariations of an additive function on a Boolean ring, Colloq. Math. 117 (2009), 267-279.
• Semivariations of a vectore measure, Acta Sci. Math. (Szeged) 76 (2010), 411--425.
• Cardinality of some convex sets and of their sets of extreme points, Colloq. Math. 123 (2011), 133--147.
• (with V. Losert and J. Spurný), Uniqueness of Cartesian products of compact convex sets, Bull. Polish Acad. Sci. Math. 59 (2011), 175--183.
• Compactness and extreme points of the set of quasi-measure extensions of a quasi-measure, Dissertationes Math. 403, Warszawa 2013.
• Order boundedness and weak compactness of the set of quasi-measure extensions of a quasi-measure, Comment. Math. Univ. Carolin. 56 (2015), 331--345.
• Order-theoretic properties of some sets quasi-measures, ibidem, 58 (2017), 197-212.
• Order-theoretic properties and separability of some sets of quasi-measures, Ricerche Mat. 67 (2018), 581-595; Correction, ibidem, in press.
• Order intervals in Banach lattices and their extreme points, Colloq. Math., to appear.