New applications of Pták's extension theorem to weak compactness
Pedro José Paúl (1989)
Czechoslovak Mathematical Journal
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Displaying similar documents to “On the heredity of weak compactness in biprojective tensor product spaces”
New applications of Pták's extension theorem to weak compactness
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Let E be a metrizable locally convex topological vector space x ∈ E, and let D be a closed convex subset of E such that x ∈ D. In this paper we prove that the weakly sequentially continuous mapping F: D ∪ D which satisfies V̅ = c̅o̅n̅v̅({x} ∪ F(V))⇒ V is relatively weakly compact, has a fixed point. Employing the above results we prove the existence theorem for the Cauchy problem x'(t) = f(t,x(t)), x(0) = x₀. As compared with...