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Suppose that F is an element of H1 (Hardy class of order 1 over the unit disc) and F is a univalent starlike mapping. Let s(F) denote the set of functions subordinate to F and Hs(F) the closed convex hull of s(F). We prove that f ∈Hs(F) and ‖f‖1 = ‖F‖1 then f is an element of s(F).
We show that a separable inner product space is complete if and only if its lattice of strongly closed subspaces possesses at least one state. This gives a measure‐theoretic characterization of Hilbert spaces among inner product spaces and, as a by‐product, exhibits a ‘continuous’ example of a...
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