Geodesic
On the Exact $\mathcal{K}$-Monotonicity of Banach Couples
Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 3, pp. 60-63.

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We present necessary and sufficient conditions for a Banach couple formed by the space $L_{\infty}$ and an arbitrary Lorentz space $\Lambda(\varphi)$ to be exact $\mathcal{K}$-monotone. The proof relies on the description of the set of extreme points of a $\mathcal{K}$-orbit for appropriate finite-dimensional couples. As a consequence of this description, we obtain a generalization of a well-known Markus theorem.
Keywords: Peetre $\mathcal{K}$-functional, exact $\mathcal{K}$-monotone Banach couple, Lorentz space, rearrangement, extreme point, convex hull. 
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S. V. Astashkin. On the Exact $\mathcal{K}$-Monotonicity of Banach Couples. Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 3, pp. 60-63. http://geodesic.mathdoc.fr/item/FAA_2002_36_3_a6/

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