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On twisted Fréchet and (LB)-spaces

Authors: G. Metafune and V. B. Moscatelli
Journal: Proc. Amer. Math. Soc. 108 (1990), 145-150
MSC: Primary 46A06; Secondary 46A12, 46A20, 46A32
MathSciNet review: 984806
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Abstract: We study twisted Fréchet spaces as well as twisted $ (LB)$-spaces. We prove that a twisted space can have a nontwisted dual and that twisted spaces of a special class cannot be complemented in nontwisted spaces. We also give new examples of twisted spaces.

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  • [1] J. Bonet and S. Dierolf, A note on biduals of strict $ (LB)$-spaces, Resultate Math. (to appear).
  • [2] -, On (LB)-spaces of Moscatelli type, Doga Bilim Dergisi. Ser. $ {{\text{A}}_1}$: Mat. Fiz. Kim. Astronom. Yerbilim (to appear).
  • [3] -, On Fréchet spaces of Moscatelli type, preprint.
  • [4] J. C. Diaz, Continuous norms in Fréchet lattices, Arch. Math. (to appear).
  • [5] S. Dierolf, On spaces of continuous linear mappings between locally convex spaces, Note Mat. 5 (1985), 147-255. MR 863525 (88b:46014)
  • [6] S. Dierolf and V. B. Moscatelli, A Fréchet space which has a continuous norm but whose bidual does not, Math. Z. 191 (1986), 17-21. MR 812599 (87d:46004)
  • [7] K. Floret and V. B. Moscatelli, On bases in strict inductive and projective limits of locally convex spaces, Pacific J. Math. 119 (1985), 103-113. MR 797017 (87a:46011)
  • [8] -, Unconditional bases in Fréchet spaces, Arch. Math. 47 (1986), 129-130. MR 859262 (87m:46009)
  • [9] A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc., no. 16, Amer. Math. Soc., Providence, R.I., 1955. MR 0075539 (17:763c)
  • [10] H. Jarchow, Locally convex spaces, Teubner Studienbüch. Math., Stuttgart, 1981. MR 632257 (83h:46008)
  • [11] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces II, Springer, Berlin, 1979. MR 540367 (81c:46001)
  • [12] -, Classical Banach spaces, Lecture notes in Math., Springer, Berlin, 1973. MR 0415253 (54:3344)
  • [13] G. Metafune and V. B. Moscatelli, A twisted Fréchet space with basis, Monatsh. Math. 105 (1988), 127-129. MR 930431 (89b:46010)
  • [14] -, Complemented subspaces of sums and products of Banach spaces, Ann. Mat. Pura Appl. 153 (4) (1989), 1-16.
  • [15] -, Another construction of twisted spaces, Proc. Roy. Irish. Acad. Sect. A 87 (1987), 163-168. MR 941711 (89g:46005)
  • [16] V. B. Moscatelli, Fréchet spaces without continuous norms and without bases, Bull. London Math. Soc 12 (1980), 63-66. MR 565487 (81d:46003)
  • [17] J. Taskinen, Counterexamples to "Problème des topologies" of Grothendieck, Ann. Acad. Sci. Fenn. Ser. A I Math., no. 63, 1986, pp. 1-25. MR 879646 (88h:46131)
  • [18] D. Vogt and M. J. Wagner, Charakterisierung der Unterräume und Quotientenräume der nuklearen stabilen Potenzreihenräume von unendlichem Typ, Studia Math. 70 (1981), 63-80. MR 646960 (83e:46011)

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