Dieudonné-Schwartz theorem on bounded sets in inductive limits. II
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- by J. Kučera and C. Bosch PDF
- Proc. Amer. Math. Soc. 86 (1982), 392-394 Request permission
Abstract:
The Dieudonné-Schwartz Theorem [1, Chapter 2, §12] has been stated for strict inductive limits. In [3] it has been extended to inductive limits. Here the result of [3] is generalized. Also, the case when each set bounded in ind lim ${E_n}$ is contained, but not necessarily bounded, in some ${E_n}$ is considered.References
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J. Horváth, Topological vector spaces and distributions, Vol. 1, Addison-Wesley, Reading, Mass., 1966.
- J. Kučera and K. McKennon, Bounded sets in inductive limits, Proc. Amer. Math. Soc. 69 (1978), no. 1, 62–64. MR 463937, DOI 10.1090/S0002-9939-1978-0463937-1
- J. Kučera and K. McKennon, Dieudonné-Schwartz theorem on bounded sets in inductive limits, Proc. Amer. Math. Soc. 78 (1980), no. 3, 366–368. MR 553378, DOI 10.1090/S0002-9939-1980-0553378-X
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 392-394
- MSC: Primary 46A12
- DOI: https://doi.org/10.1090/S0002-9939-1982-0671201-1
- MathSciNet review: 671201