Axioms of determinacy and biorthogonal systems
- 44 Downloads
If allΠn1 games are determined, every non-norm-separable subspaceX ofl∞(N) which is W* —Σn+1/1 contains a biorthogonal system of cardinality 2ℵ0. In Levy’s model of Set Theory, the same is true of every non-norm-separable subspace ofl∞(N) which is definable from reals and ordinals. Under any of the above assumptions,X has a quotient space which does not linearly embed into 1∞(N).
Unable to display preview. Download preview PDF.
- 3.D. Gale and F. M. Stewart,Infinite games with perfect information, inContributions to the Theory of Games, Ann. Math. Studies28, Princeton, 1953.Google Scholar
- 5.K. Kunen,On hereditarily Lindelöf Banach spaces, manuscript, July 1980.Google Scholar
- 6.A. Levy,Definability in axiomatic set theory I, inLogic, Methodology and Philosophy of Science (Y. Bar-Hillel, ed.), North-Holland, Amsterdam, 1965, pp. 127–151.Google Scholar
- 7.J. Lindenstrauss and L. Tzafriri,Classical Banach Spaces, Vol. 1,Sequence Spaces, Springer-Verlag, Berlin, 1977, p. 92.Google Scholar
- 9.A. I. Markushevich,On a basis in the wide sense for linear spaces, Dokl. Akad. Nauk SSSR41 (1943), 241–244.Google Scholar
- 11.S. Negrepontis,Banach spaces and topology, inHandbook of Set-theoretic Topology (K. Kunen and J. E. Vaughan, eds.), North-Holland, Amsterdam, 1984, pp. 1045–1142.Google Scholar
- 14.G. A. Suarez,Some uncountable structures and the Choquet-Edgar property in non separable Banach spaces, Proc. of the 10th Spanish-Portugese Conf. in Math. III, Murcia, 1985, pp. 397–406.Google Scholar