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Extreme compact operators from Orlicz spaces to C ( Ω )

Shutao Chen, Marek Wisła (1993)

Commentationes Mathematicae Universitatis Carolinae

Let E ϕ ( μ ) be the subspace of finite elements of an Orlicz space endowed with the Luxemburg norm. The main theorem says that a compact linear operator T : E ϕ ( μ ) → C ( Ω ) is extreme if and only if T * ω ∈ Ext B ( ( E ϕ ( μ ) ) * ) on a dense subset of Ω , where Ω is a compact Hausdorff topological space and 〈 T * ω , x 〉 = ( T x ) ( ω ) . This is done via the description of the extreme points of the space of continuous functions C ( Ω , L ϕ ( μ ) ) , L ϕ ( μ ) being an Orlicz space equipped with the Orlicz norm (conjugate to the Luxemburg one). There is also given a theorem on closedness of the set of extreme...

Extreme points of the complex binary trilinear ball

Fernando Cobos, Thomas Kühn, Jaak Peetre (2000)

Studia Mathematica

We characterize all the extreme points of the unit ball in the space of trilinear forms on the Hilbert space ℂ 2 . This answers a question posed by R. Grząślewicz and K. John [7], who solved the corresponding problem for the real Hilbert space ℝ 2 . As an application we determine the best constant in the inequality between the Hilbert-Schmidt norm and the norm of trilinear forms.

Extremely non-complex Banach spaces

Miguel Martín, Javier Merí (2011)

Open Mathematics

A Banach space X is said to be an extremely non-complex space if the norm equality ∥Id +T 2∥ = 1+∥T 2∥ holds for every bounded linear operator T on X. We show that every extremely non-complex Banach space has positive numerical index, it does not have an unconditional basis and that the infimum of diameters of the slices of its unit ball is positive.

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