On bounded sets in inductive limits of normed spaces

On bounded sets in inductive limits of normed spaces
HTML articles powered by AMS MathViewer

by Klaus Floret PDF

Proc. Amer. Math. Soc. 75 (1979), 221-225 Request permission

A theorem on bounded sets in locally convex inductive limits is proven and applied in various special cases.

References

M. De Wilde, Sur un type particulier de limite inductive, Bull. Soc. Roy. Sci. Liège 35 (1966), 545–551 (French, with English summary). MR 215045
E. Dubinsky, Echelon spaces of order $\infty$, Proc. Amer. Math. Soc. 16 (1965), 1178–1183. MR 185428, DOI 10.1090/S0002-9939-1965-0185428-9
Ed Dubinsky, Projective and inductive limits of Banach spaces, Studia Math. 42 (1972), 259–263. MR 310578, DOI 10.4064/sm-42-3-259-263
Klaus Floret, Lokalkonvexe Sequenzen mit kompakten Abbildungen, J. Reine Angew. Math. 247 (1971), 155–195 (German). MR 287271, DOI 10.1515/crll.1971.247.155
Klaus Floret, Folgenretraktive Sequenzen lokalkonvexer Räume, J. Reine Angew. Math. 259 (1973), 65–85 (German). MR 313748, DOI 10.1515/crll.1973.259.65
Klaus Floret and Joseph Wloka, Einführung in die Theorie der lokalkonvexen Räume, Lecture Notes in Mathematics, No. 56, Springer-Verlag, Berlin-New York, 1968 (German). MR 0226355
Alexandre Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955), Chapter 1: 196 pp.; Chapter 2: 140 (French). MR 75539
Richard B. Holmes, Geometric functional analysis and its applications, Graduate Texts in Mathematics, No. 24, Springer-Verlag, New York-Heidelberg, 1975. MR 0410335
Hikosaburo Komatsu, Projective and injective limits of weakly compact sequences of locally convex spaces, J. Math. Soc. Japan 19 (1967), 366–383. MR 217557, DOI 10.2969/jmsj/01930366

Topological vector spaces

Heinrich P. Lotz, N. T. Peck, and Horacio Porta, Semi-embeddings of Banach spaces, Proc. Edinburgh Math. Soc. (2) 22 (1979), no. 3, 233–240. MR 560985, DOI 10.1017/S0013091500016394
B. M. Makarov, Some pathological properties of inductive limits of $B$-spaces, Uspehi Mat. Nauk 18 (1963), no. 3 (111), 171–178 (Russian). MR 0152867