Abstract
Letτ be a cardinal with cf(τ)>ℵ0. Then a Banach spaceE contains a subspace isomorphic tol l(τ) if and only if [0,1]r is a continuous image of the unit ballE′1 ofE′, provided with the w*-topology. It follows that, for each cardinalκ, ifE′1 contains a copy ofβκ, thenE has a quotient isomorphic tol ∞(κ). In this situation we show thatE has even a quotientisometric tol ∞(κ).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Bibliographie
S. Argyros et S. Negropontis,Universal embeddings of l l∞ into (X) andL α(μ), Topology, Vol. 1, 4th Colloquium Budapest 1978, Colloq. Math. Soc. Janos Bolyai 23, 1980, pp. 75–128.
P. Erdös et R. Rado,Intersection theorems for systems of sets, J. London Math. Soc.35 (1960), 85–90;Part II, J. London Math. Soc.44 (1969), 467–479.
J. Hagler,On the structure of S and C(S) for S dyadic, Trans. Amer. Math. Soc.214 (1975), 415–428.
R. Haydon,On Banach spaces containing l l(τ) and types of measures on compact spaces, Israel J. Math.28 (1977), 313–324.
J. R. Partington,Equivalent norms on spaces of bounded functions, Israel J. Math.35 (1980), 205–209.
H. P. Rosenthal,A characterisation of Banach spaces containing l l, Proc. Nat. Acad. Sci. U.S.A.71 (1974), 2411–2413.
M. Talagrand,Non existence de certaines sections mesurables et contre-exemples en théorie du relèvement, Proceedings “Measure Theory, Oberwolfach 1979”, Lecture Notes in Math.794, Springer-Verlag, 1980.
M. Talagrand,Un nouveau C(K) de Grothendieck, Israel J. Math.37 (1980), 181–191.
M. Talagrand,Sur les mesures définies par une application Pettis-integrable, Bull. Soc. Math. France108 (1980), 475–483.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Talagrand, M. Sur les espaces de Banach contenantl 1(τ). Israel J. Math. 40, 324–330 (1981). https://doi.org/10.1007/BF02761372
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02761372