Previous |  Up |  Next

Article

Keywords:
locally convex Riesz space; short exact sequence; three-space-problem
Summary:
We investigate the stability of some properties of locally convex Riesz spaces in connection with subspaces and quotients and also the corresponding three-space-problems. We show that in the richer structure there are more positive answers than in the category of locally convex spaces.
References:
[1] Bonet J., Dierolf S.: On the lifting of bounded sets in Fréchet spaces. Proc. Edinburgh Math. Soc. 36 (1993), 277-281. MR 1221048 | Zbl 0792.46001
[2] Bonet J., Dierolf S., Fernandez C.: On the three-space-problem for distinguished Fréchet spaces. Bull. Soc. Roy. Sci. Liège 59 (1990), 301-306. MR 1070413 | Zbl 0713.46001
[3] Diaz J.C., Dierolf S., Domanski P., Fernandez C.: On the three-space-problem for dual Fréchet spaces. Bull. Polish Acad. Sci. 40 (1992), 221-224. MR 1401875 | Zbl 0783.46002
[4] Dierolf S.: On the three-space-problem and the lifting of bounded sets. Collect. Math. 44 (1993), 81-89. MR 1280727 | Zbl 0803.46001
[5] Graev M.I.: Theory of topological groups. Uspekhi Mat. Nauk 5 (1950), 3-56. MR 0036245
[6] Grothendieck A.: Sur les espaces (F) et (DF). Summa Bras. Math. 3 (1954), 57-123. MR 0075542 | Zbl 0058.09803
[7] Husain T., Khaleelulla S.M.: Barrelledness in Topological and Ordered Vector Spaces, Lecture Notes in Mathematics 692. Springer Berlin-Heidelberg-New York (1978). MR 0520916
[8] Kawai I.: Locally convex lattices. J. Math. Soc. Japan 9 (1957), 281-314. MR 0095399 | Zbl 0079.32203
[9] Köthe G.: Topological Vector Spaces I, $2^{nd}$ ed. Springer Berlin-Heidelberg-New York (1983). MR 0248498
[10] Meise R., Vogt D.: Einführung in Funktionalanalysis. Vieweg Wiesbaden (1992). MR 1195130
[11] Peressini A.L.: On topologies in ordered vector spaces. Math. Annalen 144 (1961), 199-223. MR 0138982 | Zbl 0099.09103
[12] Roelcke W., Dierolf S.: On the three-space-problem for topological vector spaces. Collect. Math. 32 (1981), 13-35. MR 0643398 | Zbl 0489.46002
[13] Shaefer H.H.: Topological Vector Spaces. Springer Berlin-Heidelberg-New York (1970).
[14] Wong Y-C., Ng K-F.: Partially Ordered Topological Vector Spaces, Oxford Mathematical Monographs. Clarendon Press Oxford (1973). MR 0454581
Partner of
EuDML logo