Available in electronic format
Available in print format		 Transacrions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Copies of $c_{0}$ and $\ell _{\infty }$ in topological Riesz spaces

Author(s): Lech Drewnowski; Iwo Labuda
Journal: Trans. Amer. Math. Soc. 350 (1998), 3555-3570.
MSC (1991): Primary 46A40, 46E30, 46B42, 28B05, 40A99
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: The paper is concerned with order-topological characterizations of topological Riesz spaces, in particular spaces of measurable functions, not containing Riesz isomorphic or linearly homeomorphic copies of $c_{0}$ or $\ell _{\infty }$.

References:

[AB1]
C. Aliprantis and O. Burkinshaw, Locally solid Riesz spaces, Academic Press, 1978. MR 58:12271

[AB2]
-, Positive operators, Academic Press, 1985. MR 87h:47086

[BL]
G. Buskes and I. Labuda, On Levi-like properties and some of their applications in Riesz space theory, Canad. Math. Bull. 31 (1988), 477-486. MR 90a:46009

[C]
A. Costé, Convergence des séries dans les espaces $F$-normés de fonctions mesurables, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 19 (1971), 131-134. MR 44:5425

[Di]
S. Díaz, On Schwartz's C-spaces and Orlicz's O-spaces, Colloq. Math. 64 (1993), 245-251.

[D1]
L. Drewnowski, Equivalence of Brooks-Jewett, Vitali-Hahn-Saks and Nikodym theorems, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 20 (1972), 725-731. MR 47:431

[D2]
-, On subseries convergence in some function spaces, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 22 (1974), 797-803. MR 51:1366

[D3]
-, Un théorème sur les opèrateurs de $l_{\infty }(\Gamma )$, C. R. Acad. Sci. Paris Ser. A 281 (1975), 967-969. MR 52:6486

[DL1]
L. Drewnowski and I. Labuda, The Orlicz-Pettis theorem for topological Riesz spaces, Proc. Amer. Math. Soc. (to appear).

[DL2]
-, Spaces of Bochner measurable functions, Preprint (1996).

[F]
D. H. Fremlin, Topological Riesz Spaces and Measure Theory, Cambridge Univ. Press, Cambridge, 1974. MR 56:12824

[K]
N. J. Kalton, Exhaustive operators and vector measures, Proc. Edinburgh Math. Soc. 19 (1974), 291-300. MR 52:8936

[KA]
L. Kantorovich and G. Akilov, Functional Analysis (2nd, ed.), Pergamon Press, Oxford, 1982. MR 83h:46002

[L1]
I. Labuda, Exhaustive measures in arbitrary topological vector spaces, Studia Math. 58 (1976), 239-248. MR 53:8789

[L2]
-, Spaces of measurable functions, Comment. Math. (Tomus spec. in honorem Ladislai Orlicz II) (1979), 217-249. MR 81j:46037

[L3]
-, Submeasures and locally solid topologies on Riesz spaces, Math. Z. 195 (1987), 179-196. MR 88j:46009

[LA]
E. Langford and C. D. Aliprantis, Regularity properties of quotient Riesz seminorms, Indagationes Math. 78 (1975), 199-212. MR 51:6356

[MO]
W. Matuszewska and W. Orlicz, A note on modular spaces. IX, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 16 (1968), 801-808. MR 39:3278

[O1]
W. Orlicz, Über die Divergenz von allgemeinen Orthogonalreihen, Studia Math. 4 (1933), 27-32.

[O2]
-, On a class of asymptotically divergent sequences of functions, Studia Math. 12 (1951), 286-307. MR 13:936d

[R]
H. P. Rosenthal, On relatively disjoint families of measures, with some applications to Banach space theory, Studia Math. 37 (1970), 13-36. MR 42:5015

[S]
L. Schwartz, Un théorème de convergence dans les $L^{p}$, $0\leqslant p<\infty $, C. R. Acad. Sci. Paris 268 A (1969), 704-706. MR 39:1958

[VG]
A. I. Veksler and V. A. Geiler, Order and disjoint completeness of linear partially ordered spaces, Siberian Math. J. (1972), 30-35. MR 45:5713

[Wn]
W. Wnuk, Locally solid Riesz spaces not containing $c_{0}$, Bull. Polish Acad. Sci., Mathematics 36 (1988), 51-56. MR 90g:46015

[Wo]
W. A. Woyczy\'{n}ski, Sur la convergence des séries dans les espaces de type $(L)$, C. R. Acad. Sci. Paris 268 A (1969), 1254-1257. MR 39:6049

Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 46A40, 46E30, 46B42, 28B05, 40A99

Retrieve articles in all Journals with MSC (1991): 46A40, 46E30, 46B42, 28B05, 40A99

Additional Information:

Lech Drewnowski
Affiliation: Faculty of Mathematics and Computer Science, A. Mickiewicz University, Matejki 48/49, 60--769 Poznan, Poland
Email: drewlech@math.amu.edu.pl

Iwo Labuda
Affiliation: Department of Mathematics, University of Mississippi, University, Missouri 38677
Email: mmlabuda@vm.cc.olemiss.edu

DOI: 10.1090/S0002-9947-98-02157-6
PII: S 0002-9947(98)02157-6
Keywords: Topological Riesz space, space of measurable functions, Lebesgue property, Levi property, Orlicz-Pettis theorem, copy of $c_{0}$, copy of $\ell _{\infty }$
Received by editor(s): September 9, 1996
Additional Notes: The paper was written while the first author held a visiting position in the Department of Mathematics, University of Mississippi, in the Spring and Fall Semesters of 1996. He was also partially supported by the State Committee for Scientific Research (Poland), grant no 2 P301 003 07.
Copyright of article: Copyright 1998, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google