Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1994-1995 | 112 | 2 | 189-194
Tytuł artykułu

On sequential convergence in weakly compact subsets of Banach spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
We construct an example of a Banach space E such that every weakly compact subset of E is bisequential and E contains a weakly compact subset which cannot be embedded in a Hilbert space equipped with the weak topology. This answers a question of Nyikos.
  • Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
  • [AF] S. Argyros and V. Farmaki, On the structure of weakly compact subsets of Hilbert spaces and applications to the geometry of Banach spaces, Trans. Amer. Math. Soc. 289 (1985), 409-427.
  • [BFT] J. Bourgain, D. H. Fremlin and M. Talagrand, Pointwise compact sets of Baire-measurable functions, Amer. J. Math. 100 (1978), 845-886.
  • [DFJP] W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński, Factoring weakly compact operators, J. Funct. Anal. 17 (1974), 311-327.
  • [Go] G. Godefroy, Compacts de Rosenthal, Pacific J. Math. 91 (1980), 293-306.
  • [LS] A. G. Leiderman and G. A. Sokolov, Adequate families of sets and Corson compacts, Comment. Math. Univ. Carolin. 25 (1984), 233-245.
  • [Ma] W. Marciszewski, On a classification of pointwise compact sets of the first Baire class functions, Fund. Math. 133 (1989), 195-209.
  • [Mi] E. Michael, A quintuple quotient test, Gen. Topology Appl. 2 (1972), 91-138.
  • [Ne] S. Negrepontis, Banach spaces and topology, in: Handbook of Set-Theoretic Topology, North-Holland, 1984, 1045-1142.
  • [Ny1] P. Nyikos, Classes of compact sequential spaces, in: Set Theory and its Applications, Lecture Notes in Math. 1401, Springer, 1989, 135-159.
  • [Ny2] P. Nyikos, Properties of Eberlein compacta, Abstracts of Eighth Summer Conference on General Topology and Applications, 1992, 28.
  • [Po] R. Pol, Note on pointwise convergence of sequences of analytic sets, Mathematika 36 (1989), 290-300.
Typ dokumentu
Identyfikator YADDA
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.