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Some results on intersection properties of balls in complex Banach spaces. (English) Zbl 0645.46021

Predual real \(L^ 1\)-spaces are characterized by the 4.2 intersection property. The structure of real spaces with the 3.2 intersection property and of real and complex spaces with the 4.3 intersection property is fairly well understood. In this paper we study complex spaces with the n.k. intersection property when \(n>k\geq 4\). We show that the 5.4. intersection property characterizes complex \(L^ 1\)-preduals, and that the \((2n+1).2n\). intersection property implies the almost \((2n+1).(2n- 1)\). intersection property in the complex case.

MSC:

46B25 Classical Banach spaces in the general theory
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46B10 Duality and reflexivity in normed linear and Banach spaces
46B20 Geometry and structure of normed linear spaces
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