Dual local completeness

Proceedings of the American Mathematical Society

Volumn 125, Issue 4, 1997, Pages 1063-1070

  Saxon, Stephen A ^a   Sanchez Ruiz L M ^b  

^a UNIVERSITY OF FLORIDA   (United States)

^b UNIVERSITAT POLITÈCNICA DE VALÈNCIA   (Spain)

Author keywords

Barrelled; Dual locally complete; Properties (l) and (lc)

Indexed keywords

EID: 21744460534     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-97-03864-1     Document Type: Article

References (22)

1. M. De Wilde and C. Houet, On increasing sequences of absolutely convex sets in locally convex spaces, Math. Ann. 192(1971), 257-261. MR 44:5746
2. J. C. Ferrando, M. Löpez Pellicer and L. M. Sânchez Ruiz, Metrizable Barrelled Spaces, Pitman RNMS 332, Longman, 1995. CMP 96:09
3. T. Husain, Two new classes of locally convex spaces, Math. Ann. 166(1966), 289-299. MR 35:3406
4. N. J. Kalton, Some forms of the closed graph theorem, Proc. Camb. Phil. Soc. 70(1971), 401-408. MR 46:634
5. G. Köthe, Topological Vector Spaces I, Springer-Verlag, 1969. MR 40:1750
6. M. Kunzinger, Barrellediiess, Baire-like-, and (LF)-spaces, Pitman RNMS 298, Longman, 1993. MR 95e:46004
7. P. Pérez Carreras and J. Bonet, Barrelled Locally Convex Spaces, Math. Studies 131, North Holland, 1987. MR 88j:46003
8. W. Roelcke, On the finest locally convex topology agreeing with a given topology on a sequence of absolutely convex sets, Math. Ann. 198(1974), 57-80. MR 48:2705
9. W. Ruess, A Grothendiech representation for the completion of cones of continuous seminorms, Math. Ann. 208(1974), 71-90. MR 50:14147
10. W. Ruess, Generalized inductive limit topologies and barrelledness properties, Pac. J. Math. 63, no. 2(1976), 499-516. MR 54:3348
11. W. Ruess, Closed graph theorems for generalized inductive limit topologies, Math. Proc. Camb. Phil. Soc. 82(1977), 67-83. MR 56:3612
12. S. Saxon, Basis Cone Base Theory, Doctoral Dissertation, Florida State University, Tallahassee, Fla., 1969.
13. S. Saxon, Nuclear and product spaces, Baire-like spaces, and the strongest locally convex topology, Math. Ann. 197(1972), 87-106. MR 46:4140
14. S. A. Saxon and M. D. Levin, Every countable-codimensional subspace of a barrelled space is a barrelled space, Abstract 660-44, Notices of the Amer. Math. Soc. 15(1968), 1020.
15. S. Saxon and M. Levin, Every countable-codimensional subspace of a barrelled space is barrelled, Proc. Amer. Math. Soc. 29(1971), 91-96. MR 43:6691
16. M. Valdivia, Absolutely convex sets in barrelled spaces, Ann. Inst. Fourier 21(1971), 3-13. MR 48:11968
17. M. Valdivia, Mackey convergence and the closed graph theorem, Arch. Math. 25(1974), 649-656. MR 51:11052
18. M. Valdivia, On quasi-completeness and sequential completeness in locally convex spaces, 3. Reine Angew. Math. 276(1975), 190-199. MR 52:8870
19. M. Valdivia, Topics in Locally Convex Spaces, Math. Studies 67, North Holland, 1982. MR 84i:46007
20. J. H. Webb, Sequential convergence in locally convex spaces, Proc. Camb. Phil. Soc. 64(1968), 341-364. MR 36:5652
21. J. H. Webb, Countable-codimensional subspaces of locally convex spaces, Proc. Edinb. Math. Soc. 18(1973), 167-172. MR 47:7370
22. A. Wilansky, Modern Methods in Topological Vector Spaces, McGraw-Hill, 1978. MR 81d:46001