Weakly Compact Generating and Shrinking Markusevic Bases

It is shown that most of the well known classes of nonseparable Ba-nach spaces related to the weakly compact generating can be charac-terized by elementary properties of the closure of the coefficient space of Markuševic ̌ bases for such spaces. In some cases, such property is then shared by all Markuševic ̌ bases in the space. Let X be a Banach space and let 〈 ·, · 〉 denote the canonical duality pairing between X and its dual space X∗. A system {xγ;x∗γ}γ∈Γ, where xγ ∈ X, x∗γ ∈ X∗, γ ∈ Γ, is called a Markuševic ̌ basis for X if 〈xγ, x∗γ 〉 = 1 for every γ ∈ Γ, 〈xγ, x∗γ′ 〉 = 0 whenever γ, γ ′ ∈ Γ and γ 6 = γ′, the linear span sp{xγ; γ ∈ Γ} is dense in X and sp{x∗γ; γ ∈ Γ} is weak ∗ dense in X∗. A compact spaceK is a Corson compact if for some set Γ, K is homeomorphic to a subset T of a product [−1, 1]Γ taken in its pointwise topology, such that

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