Normed barrelled spaces

• Autorzy: Christopher E. Stuart
• Języki publikacji: EN

Abstrakty

EN

In this paper we present a general "gliding hump" condition that implies the barrelledness of a normed vector space. Several examples of subspaces of $l^1$ are shown to be barrelled using the theorem. The barrelledness of the space of Pettis integrable functions is also implied by the theorem (this was first shown in [3]).

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2000
• Tom: 53
• Numer: 1
• Strony: 205-210

Daty

wydano

2000

Twórcy

autor

Christopher E. Stuart

• Department of Mathematical Sciences, Eastern New Mexico University, Station 18, Portales, NM 88130, U.S.A.

Bibliografia

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• [3] L. Drewnowski, M. Florencio, and P. J. Paul, The space of Pettis integrable functions is barrelled, Proc. Amer. Math. Soc. 114 (1992), 687-694.
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• [7] S. Saxon, Some normed barrelled spaces which are not Baire, Math. Ann. 209 (1974), 153-160.
• [8] C. Stuart, Dense barrelled subspaces of Banach spaces, Collect. Math. 47 (1996), 137-143.
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