(LF)-spaces with more-than-separable quotients

Journal of Mathematical Analysis and Applications

Volumn 434, Issue 1, 2016, Pages 12-19

  Saxon, Stephen A ^a  

^a UNIVERSITY OF FLORIDA   (United States)

Author keywords

(LF) spaces; Primitive spaces; Properly separable quotients

Indexed keywords

EID: 84943364946     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2015.09.005     Document Type: Article

References (20)

1. Amemiya I., Komura Y. Über nicht-vollständige Montel Räume. Math. Ann. 1968, 177:273-277.
2. Carreras P.Pérez, Bonet J. Una nota sobre un resultado de Eidelheit. Collect. Math. 1982, 33:195-199.
3. Eberhardt V., Roelcke W. Über einem Graphensatz für lineare abbildungen mit metrisierbarem Zielraum. Manuscripta Math. 1974, 13:53-68.
4. Eidelheit M. Zur Theorie der Systeme linearer Gleichungen. Studia Math. 1936, 6:130-148.
5. Ferrando J.C., Kakol Jerzy, Saxon Stephen A. Characterizing P-spaces X in terms of Cp(X). J. Convex Anal. 2015, 22(4). in press.
6. Ferrando J.C., Sánchez Ruiz L.M. On sequential barrelledness. Arch. Math. 1991, 57:597-605.
7. Horváth J. Topological Vector Spaces and Distributions 1966, Addison-Wesley.
8. Kakol J., Saxon S.A., Todd A.R. Barrelled spaces with(out) separable quotients. Bull. Aust. Math. Soc. 2014, 90:295-303.
9. Robertson W.J. On properly separable quotients of strict (LF) spaces. J. Aust. Math. Soc. 1989, 47:307-312.
10. Rosenthal H.P. On quasi-complemented subspaces of Banach spaces, with an appendix on compactness of operators from ℓp(μ) to ℓr(ν). J. Funct. Anal. 1969, 4:176-214.
11. Saxon S.A. Nuclear and product spaces, Baire-like spaces, and the strongest locally convex topology. Math. Ann. 1972, 197:87-106.
12. Saxon S.A. Every countable-codimensional subspace of an infinite-dimensional [non-normable] Fréchet space has an infinite-dimensional Fréchet quotient [isomorphic to ω]. Bull. Pol. Acad. Sci. 1991, 39:161-166.
13. 1. Bull. Pol. Acad. Sci. 1991, 39:167-173.
14. Saxon S.A., Levin Mark Every countable-codimensional subspace of a barrelled space is barrelled. Proc. Amer. Math. Soc. 1971, 29:91-96.
15. Saxon S.A., Narayanaswami P.P. Metrizable (LF)-spaces, (db)-spaces and the separable quotient problem. Bull. Aust. Math. Soc. 1981, 23:65-80.
16. Saxon S.A., Narayanaswami P.P. (LF)-spaces, quasi-Baire spaces, and the strongest locally convex topology. Math. Ann. 1986, 274:627-641.
17. Saxon S.A., Narayanaswami P.P. Metrizable [normable] (LF)-spaces and two classical problems in Fréchet [Banach] spaces. Studia Math. 1989, 93:1-16.
18. S.A. Saxon, L.M. Sánchez Ruiz, Reinventing weak barrelledness, preprint.
19. Saxon S.A., Tweddle I. The fit and flat components of barrelled spaces. Bull. Aust. Math. Soc. 1995, 51:521-528.
20. Saxon S.A., Wilansky A. The equivalence of some Banach space problems. Colloq. Math. 1977, XXXVII:217-226.