Weak$^ *$ convergence in higher duals of Orlicz spaces
HTML articles powered by AMS MathViewer
- by Denny H. Leung PDF
- Proc. Amer. Math. Soc. 103 (1988), 797-800 Request permission
Abstract:
It is shown that the spaces ${\left ( {\Sigma \oplus E} \right )_{{l^\infty }(\Gamma )}}$ are Grothendieck spaces for a class of Banach lattices $E$ which includes the Orlicz spaces with weakly sequentially complete duals.References
- Jean Bourgain, New classes of ${\cal L}^{p}$-spaces, Lecture Notes in Mathematics, vol. 889, Springer-Verlag, Berlin-New York, 1981. MR 639014
- Burkhard Kühn, Schwache Konvergenz in Banachverbänden, Arch. Math. (Basel) 35 (1980), no. 6, 554–558 (1981) (German). MR 604255, DOI 10.1007/BF01235381 D. H. Leung, Uniform convergence of operators and Grothendieck spaces with the Dunford-Pettis property, Ph.D. Thesis, Univ. of Illinois, 1987.
- Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. I, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 92, Springer-Verlag, Berlin-New York, 1977. Sequence spaces. MR 0500056, DOI 10.1007/978-3-642-66557-8
- Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. II, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 97, Springer-Verlag, Berlin-New York, 1979. Function spaces. MR 540367, DOI 10.1007/978-3-662-35347-9 H. P. Lotz, Weak* convergence in the dual of weak ${L^p}$, preprint.
- Frank Räbiger, Beiträge zur Strukturtheorie der Grothendieck-Räume, Sitzungsberichte der Heidelberger Akademie der Wissenschaften. Mathematisch-Naturwissenschaftliche Klasse [Reports of the Heidelberg Academy of Science. Section for Mathematics and Natural Sciences], vol. 85, Springer-Verlag, Berlin, 1985 (German). MR 828457, DOI 10.1007/978-3-642-45612-1
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 797-800
- MSC: Primary 46E30; Secondary 46B20
- DOI: https://doi.org/10.1090/S0002-9939-1988-0947660-9
- MathSciNet review: 947660