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Markov operators on the space of vector measures; coloured fractals

Karol Baron, Andrzej Lasota (1998)

Annales Polonici Mathematici

We consider the family 𝓜 of measures with values in a reflexive Banach space. In 𝓜 we introduce the notion of a Markov operator and using an extension of the Fortet-Mourier norm we show some criteria of the asymptotic stability. Asymptotically stable Markov operators can be used to construct coloured fractals.

Means of vector-valued functions and projections which commute with the action of a group

J. F. Price (1972)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Measurability and Pettis integration in Hilbert spaces.

P. Masani (1978)

Journal für die reine und angewandte Mathematik

Measurable multifunctions and their applications to convex integral functionals.

Papageorgiou, Nikolaos S. (1989)

International Journal of Mathematics and Mathematical Sciences

Measures on orthomodular vector space lattices

Hans Keller (1988)

Studia Mathematica

Measures which agree on balls.

J. Hoffmann-Jorgensen (1975)

Mathematica Scandinavica

Measures with finite semi-variation.

Debiève, C. (1997)

Bulletin of the Belgian Mathematical Society - Simon Stevin

Mengenwertige Masse und Fortsetzungen.

Werner Rupp (1977)

Manuscripta mathematica

Mesures de Radon à valeurs vectorielles

P. Magnier (1970/1971)

Séminaire Équations aux dérivées partielles (Polytechnique)

Mesures vectorielles et partitions continues de l'unité

Danièle Bucchioni (1975)

Publications du Département de mathématiques (Lyon)

Moment Sequences in Locally Convex Spaces.

Anthony K. Whitford (1973)

Mathematische Annalen

Monoidwertige Integrale

Wolfgang J. Marik (1987)

Czechoslovak Mathematical Journal

Monotone and convex $H^{*}$ -algebra valued functions.

Saworotnow, Parfeny P. (1996)

International Journal of Mathematics and Mathematical Sciences

Multilinear integration of bounded scalar valued functions

Ivan Dobrakov (1999)

Mathematica Slovaca

Multilinear operators on $C (K, X)$ spaces

Ignacio Villanueva (2004)

Czechoslovak Mathematical Journal

Given Banach spaces $X$ , $Y$ and a compact Hausdorff space $K$ , we use polymeasures to give necessary conditions for a multilinear operator from $C (K, X)$ into $Y$ to be completely continuous (resp. unconditionally converging). We deduce necessary and sufficient conditions for $X$ to have the Schur property (resp. to contain no copy of $c_{0}$ ), and for $K$ to be scattered. This extends results concerning linear operators.

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