Weak* derived sets of sets of linear functionals
- 32 Downloads
For a Banach space X the w*-sequential closure operator in the adjoint space is, in general, not the topological closure operator. That is, it may happen that the w*-sequential closure of a subspace T of X* is not w*-sequentially closed. The possible length of the chain of repeated w*-sequential closures of a subspace of X* in dependence on the dimension of X**/X is investigated.
KeywordsBanach Space Closure Operator Linear Functional Sequential Closure Topological Closure
Unable to display preview. Download preview PDF.
- 1.S. S. Banach, A Course of Functional Analysis [Ukrainian translation], Radyanska Shkola, Kiev (1948).Google Scholar
- 2.M. M. Day, Normed Linear Spaces, Springer-Verlag, Berlin-New York (1973).Google Scholar
- 3.P. Civin and B. Yood, “Quasireflexive spaces,” Proc. Am. Math. Soc.,8, 906–911 (1957).Google Scholar
- 4.W. J. Davis and W. B. Johnson, “Basic sequences and norming subspaces in nonquasireflexive Banach spaces,” Israel J. Math.,14, 353–367 (1973).Google Scholar
- 5.W. J. Davis and J. Lindenstrauss, “On total nonnorming subspaces,” Proc. Am. Math. Soc.,31, No. 1, 109–111 (1972).Google Scholar
- 6.A. M. Plichko, “Criteria for the quasireflexivity of a Banach space,” Dokl. Akad. Nauk Ukr. SSR,5, 406–408 (1974).Google Scholar