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Exact \(K\)-monotonicity of one class of Banach pairs. (Russian, English) Zbl 1011.46059
Sib. Mat. Zh. 43, No. 1, 14-32 (2002); translation in Sib. Math. J. 43, No. 1, 5-21 (2002).
Summary: We obtain necessary and sufficient conditions for exact \(K\)-monotonicity of a Banach pair constituted by the space of essentially bounded functions and an arbitrary Lorentz space. The proof is based on a description for the set of extreme points of \(K\)-orbits with respect to the corresponding finite-dimensional pairs.
MSC:
46M35 Abstract interpolation of topological vector spaces
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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