Weak $*$ derived sets of sets of linear functionals

B. V. Godun

Kharkiv Civil Engineering Institute

Abstract: 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 $\Gamma$ 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.

UDC: 513.88

Received: 20.05.1977

 English version: Mathematical Notes, 1978, 23:4, 333–338

Bibliographic databases:

• 
•