Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
three-space-problem; locally topological spaces; (HM)-spaces; inductively semireflexive spaces; spaces with minimal or the finest linear topology
three-space-problem; locally topological spaces; (HM)-spaces; inductively semireflexive spaces; spaces with minimal or the finest linear topology
Summary:
We examine the so-called three-space-stability for some classes of linear topological and locally convex spaces for which this problem has not been investigated.
References:
[1] Adasch N., Ernst B.: Lokaltopologische Vektorräume. Collect. Math. 25 (1974), 255-274. MR 0427994 | Zbl 0305.46006
[2] Bellenot S.F.: On nonstandard hulls of convex spaces. Can. J. Math. 28 (1976), 141-147. MR 0407556 | Zbl 0308.46001
[3] Berezanskiĭ Yu.A.: Induktivno refleksivnye lokal'no vypuklye prostranstva. Soviet Math. {Dokl.} 9 (1968), 1080-1082.
[4] Bonet J., Dierolf S.: On distinguished Fréchet spaces. Progress in Functional Analysis, K.D. Bierstedt, J. Bonet, J. Horváth, M. Maestre (eds.) Elsevier Publ. (1992), 201-214. MR 1150747 | Zbl 0785.46003
[5] Bonet J., Dierolf S., Fernandez C.: On the three-space-problem for distinguished Fréchet spaces. Bull. Soc. Roy. Sci. Liége 59 (1990), 301-306. MR 1070413 | Zbl 0713.46001
[6] Brauner K.: Duals of Fréchet spaces and a generalization of the Banach-Dieudonné theorem. Duke Math. J. 40 (1973), 845-856. MR 0330988 | Zbl 0274.46003
[7] Buchwalter H.: Espaces ultrabornologiques et b-reflexivite. Publ. Dép. Mat. Lyon 8 (1971), 91-106. MR 0320684 | Zbl 0252.46010
[8] Dierolf S.: A note on the lifting of linear and locally convex topologies on a quotient space. Collect. Math. 31 (1980), 193-198. MR 0621724 | Zbl 0453.46002
[9] Dierolf S.: On the three-space-problem and the lifting of bounded sets. Collect. Math. 44 (1993), 81-89. MR 1280727 | Zbl 0803.46001
[10] Grothendieck A.: Sur les espaces (F) et (DF). Summa Bras. Math. 3 (1954), 57-123. MR 0075542 | Zbl 0058.09803
[11] Heinrich S.: Ultrapowers of locally convex spaces and applications I. Math. Nachr. 118 (1984), 285-315. MR 0773627 | Zbl 0576.46002
[12] Henson C.W., Moore L.C., Jr.: The nonstandard theory of topological vector spaces. Trans. Amer. Math. Soc. 172 (1972), 405-435. MR 0308722
[13] Henson C.W., Moore L.C., Jr.: Invariance of the nonstandard hulls of locally convex spaces. Duke Math. J. 40 (1973), 193-205. MR 0372568 | Zbl 0256.46001
[14] Kadelburg Z.: Ultra-b-barrelled spaces and the completeness of $\Cal L_b(E,F)$. Mat. Vesnik 3 (16) (31) (1979), 23-30. MR 0589477
[15] Kadelburg Z., Radenović S.: On ultrapowers of linear topological spaces without convexity conditions. Publ. Inst. Math. (N.S) 47(61) (1990), 71-81. MR 1103531
[16] Köthe G.: Topological Vector Spaces I, $2^{nd}$ ed. Springer Berlin-Heidelberg-New York (1983). MR 0248498
[17] Meise R., Vogt D.: Einführung in Funktionalanalysis. Vieweg Wiesbaden (1992). MR 1195130
[18] Noureddine K.: Nouvelles classes d'espaces localment convexes. Publ. Dép. Mat. Lyon 10 (1973), 105-122. MR 0367605
[19] Roelcke W., Dierolf S.: On the three-space-problem for topological vector spaces. Collect. Math. 32 (1981), 13-35. MR 0643398 | Zbl 0489.46002
[20] Shaefer H.H.: Topological Vector Spaces. Springer Berlin-Heidelberg-New York (1970).
Search
Partner of
