Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On bounded sets in inductive limits of normed spaces


Author: Klaus Floret
Journal: Proc. Amer. Math. Soc. 75 (1979), 221-225
MSC: Primary 46M40; Secondary 46A25
DOI: https://doi.org/10.1090/S0002-9939-1979-0532140-X
MathSciNet review: 532140
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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


References [Enhancements On Off] (What's this?)

  • [1] M. DeWilde, Sur un type particulier de limite inductive, Bull. Soc. Roy. Sci. Liège 35 (1966), 545-551. MR 0215045 (35:5890)
  • [2] E. Dubinsky, Echelon spaces of order $ \infty $, Proc. Amer. Math. Soc. 16 (1965), 1178-1183. MR 0185428 (32:2895)
  • [3] -, Projective and inductive limits of Banach spaces, Studia Math. 42 (1972), 259-263. MR 0310578 (46:9676)
  • [4] K. Floret, Lokalkonvexe Sequenzen mit kompakten Abbildungen, J. Reine Angew. Math. 247 (1971), 155-195. MR 0287271 (44:4478)
  • [5] -, Folgenretraktive Sequenzen lokalkonvexer Raume, J. Reine Angew. Math. 259 (1973), 65-85. MR 0313748 (47:2302)
  • [6] K. Floret and J. Wloka, Einführung in die Theorie der lokalkonvexen Raume, Lecture Notes in Math., vol. 56, Springer-Verlag, Berlin and New York, 1968. MR 0226355 (37:1945)
  • [7] A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. No. 16 (1955). MR 0075539 (17:763c)
  • [8] R. B. Holmes, Geometric functional analysis and its applications, Graduate Texts in Mathematics, no. 24, Springer-Verlag, New York, 1975. MR 0410335 (53:14085)
  • [9] H. Komatsu, Projective and injective limits of weakly compact sequences of locally convex spaces, J. Math. Soc. Japan 19 (1967), 366-383. MR 0217557 (36:646)
  • [10] G. Köthe, Topological vector spaces. I, Die Grundlehren der math. Wissenschaften, Band 159, Springer-Verlag, New York, 1966.
  • [11] H. P. Lotz, N. T. Peck and H. Porta, Semi-embeddings of Banach-spaces (to appear). MR 560985 (81f:46029)
  • [12] B. M. Makarov, Pathological properties of inductive limits of Banach-spaces, Uspehi Mat. Nauk 18 (1963), 171-178 (Russian). MR 0152867 (27:2839)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46M40, 46A25

Retrieve articles in all journals with MSC: 46M40, 46A25


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0532140-X
Keywords: Locally convex inductive limits, bounded sets, sequence space, reflexive Banach-space
Article copyright: © Copyright 1979 American Mathematical Society

American Mathematical Society