Copies of R^N in F-lattices

• Autorzy: Wnuk W.

Identyfikatory

DOI

10.14708/cm.v56i2.1558

• Języki publikacji: EN

Abstrakty

EN

Modifying ideas presented in [14] we prove that a complete metrizable locally solid Riesz space E contains a linear subspace linearly homeomorphic to R^N iff E contains a sublattice order isomorphic to R^N.

Słowa kluczowe

EN

metrizable locally solid Riesz space; F-lattice; sequence spaces

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2016
• Tom: Vol 56, No. 2
• Strony: 239--242
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Wnuk W.

• Faculty of Mathematics and Computer Science, A. Mickiewicz University, Umultowska 87, 61-614 Poznan, Poland

Bibliografia

• [1] C. Aliprantis and O. Burkinshaw, Locally Solid Riesz Spaces with Applications to Economics, Mathematical Surveys and Monographs, vol. 105, American Mathematical Society 2003, DOI 10.1090/surv/105.
• [2] C. Aliprantis and O. Burkinshaw, Positive Operators, Springer Verlag 2006, DOI 10.1007/978-1-4020-5008-4.
• [3] C. Bessaga, A. Pełczyński, and S. Rolewicz, Some properties of the space (s), Colloq. Math. 7 (1959), 45-51.
• [4] L. Drewnowski and I. Labuda, Copies of co and in topological Riesz spaces, Trans. Amer. Math. Soc. 350 (1998), no. 9, 3555-3570, DOI 10.1090/S0002-9947-98-02157-6.
• [5] N. J. Kalton, N. T. Peck, and J. W. Roberts, An F-space Sampler, Cambridge University Press 1984, DOI 10.1017/CBO9780511662447.
• [6] W. A. J. Luxemburg and A. C. Zaanen, Riesz Spaces, I, North-Holland, Amsterdam 1971.
• [7] P. Meyer-Nieberg, Banach Lattices, Springer Verlag, Berlin Heidelberg New York 1991, DOI 10.1007/978-3-642-76724-1.
• [8] T. Nishiura, Completions of normed linear lattices, Colloq. Math. 19 (1968), 271-275.
• [9] S. Rolewicz, Metric Linear Spaces, Polish Scientific Publishers, Warsaw 1984.
• [10] B. Z. Vulikh and G. Ja. Lozanovskii, On metric completeness of normed and countably-normed structures, Vestnik Leningrad. Univ. 19 (1966), 12-15; in Russian.
• [11] W. Wnuk, Banach Lattices with Order Continuous Norms, Advanced Topics in Mathematics, Warsaw 1999.
• [12] M. Wójtowicz, The Sobczyk property and copies of in locally convex-solid Riesz spaces, Arch. Math. 75 (2000), 376-379, DOI 10.1007/s000130050518.
• [13] M. Wójtowicz, The lattice copies of l_1 in Banach lattices, Comment. Math. Univ. Carolinae 42 (2001), no. 4, 649-653.
• [14] M. Wójtowicz and H. Wiśniewska, Copies of sequence space w in F-lattices with applications to Musielak- -Orlicz spaces, Comment. Math. 56 (2016), no. 1,103-117, DOI 10.14708/cm.v56i1.1135.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).