Topological properties of the complex vector lattice of bounded finitely additive mesures

• Autorzy: Nowak, M.
• Języki publikacji: EN

Abstrakty

EN

Let Σ be a σ-algebra of subsets of a non-empty set Ω. Let ba(Σ) be the complex vector lattice of bounded finitely additive measures μ:Σ→C. We study locally solid topologies on ba(Σ). We develop the duality theory of ba(Σ), provided with locally convex-solid topologies.

Słowa kluczowe

EN

complex vector lattices; locally solid topologies; spaces of bounded finitely additive measures

• Czasopismo: Commentationes Mathematicae
• Rocznik: 2013
• Tom: Vol. 53, No. 2
• Strony: 271--282
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Nowak, M.

• Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, ul. Szafrana 4A, 65–516 Zielona Góra, Poland,

Bibliografia

• [1] [[AB1]] Aliprantis, C.D. and O. Burkinshaw, Positive Operators, Academic Press, New York, 1985.
• [2] [[AB2]] Aliprantis, C.D. and O. Burkinshaw, Locally solid Riesz Spaces with Applications to Economics, Second Ed., Math. Surveys and Monographs, no. 105, 2002.
• [3] [[ABo]] Aliprantis, C.D. and K.C. Border, Infinite Dimensional Analysis, Second Ed., Springer-Verlag, 1999.
• [4] [DU]] Diestel, J. and J.J. Uhl, Vector Measures, Amer. Math. Soc., Math. Surveys 15, Providence, RI, 1977.
• [5] [[F]] Fremlin, D., Topological Riesz spaces and Measure Theory, Cambridge Univ. Press, London and New York, 1974.
• [6] [[KA]] Kantorovitch, L.V. and G.P. Akilov, Functional Analysis, Pergamon Press, Oxford-Elmsford, New York, 1982.
• [7] [[N]] Nowak, M., Topological properties of the complex vector lattice of bounded measurable functions, J. Funct. Spaces Appl., vol. 2013, ID 343685.
• [8] [[S]] Schaefer, H., Banach Lattices and Positive Operators, Springer-Verlag, 1974.
• [9] [[T]] Tsoy-Wo Ma, Banach-Hilbert Spaces, Vector Measures and Group Representations, World Scientific Publishing Co. Pte. Ltd., 2002.
• [10] [[Z]] Zaanen, A.C., Riesz Spaces II, North-Holland Publ. Comp., 1983.
• [11] [[Zh]] Zhang, Xiao-Dong, On weak compactness is spaces of measures, J. Func. Anal. 143 (1997), 1–9.

Identyfikatory

DOI

10.14708/cm.v53i2.797