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. 
@article{FAA_2002_36_3_a6,
     author = {S. V. Astashkin},
     title = {On the {Exact} $\mathcal{K}${-Monotonicity} of {Banach} {Couples}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {60--63},
     publisher = {mathdoc},
     volume = {36},
     number = {3},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2002_36_3_a6/}
}
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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/