W*-derived sets of transfinite order of subspaces of dual Banach spaces

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It is an English translation of the paper originally published in Russian and Ukrainian in 1987. In the appendix of his book S.Banach introduced the following definition Let X be a Banach space and Γ be a subspace of the dual space X*. The set of all limits of w*-convergent sequences in Γ is called the w* -derived set of Γ and is denoted by Γ₍₁₎. For an ordinal α the w*- derived set of order α is defined inductively by the equality: Γ₍α₎= ᵦ<α((Γ₍ᵦ₎)₍₁₎.